(8) Lesson 7.4 - Properties of Similar Polygons
•Download as PPTX, PDF•
1 like•2,297 views
This document provides instruction on determining if two figures are similar using transformations. It includes examples of checking if figures have corresponding congruent angles and proportional sides. The document also covers the definitions of similar polygons, scale factors, and using ratios and proportions to find missing measures in similar figures.
Report
Share
Report
Share
Recommended
(8) Lesson 7.1 - Congruence and Transformations
1) The document discusses determining the coordinates of vertices after a dilation and provides examples. It also discusses congruence and using transformations like rotations, reflections, and translations to determine if two figures are congruent.
2) To determine congruence, you can use transformations to map one figure onto another. If a single or series of transformations can map all points of one figure directly onto the other, they are congruent.
3) Reflections, rotations, and translations will produce congruent figures as they preserve size and shape but change position.
Trigonometric Identities.
The document discusses three main groups of trigonometric identities: reciprocal relations which relate trig functions that are inverse of each other like tangent and cotangent; quotient relations which show relationships between ratios of trig functions like tangent being equal to the sine over the cosine; and the Pythagorean relation which is the fundamental relationship between sine and cosine where the square of one added to the square of the other is equal to 1. Examples are provided for each type of identity and an activity is included to practice using and filling in identity formulas.
6.6 proportions & similar triangles
This document discusses proportionality theorems and using similar triangles to solve problems involving segment lengths. It provides 6 theorems regarding proportional line segments in triangles and parallel lines cut by transversals. Examples are given to demonstrate using the theorems to find unknown segment lengths. Real-life applications involving building construction are also presented.
Triangle congruence
This document contains information about proving triangles congruent using various postulates and theorems of geometry including:
- SSS (side-side-side) postulate
- SAS (side-angle-side) postulate
- ASA (angle-side-angle) postulate
- AAS (angle-angle-side) theorem
- Hypotenuse-Leg theorem
It also defines key terms like hypotenuse and legs of a right triangle and presents the Pythagorean theorem.
Analytical geometry Grade 10
This document is a presentation on analytic geometry that was compiled from 6 different sources. It introduces analytic geometry and its history, developed by Descartes and Fermat in the 1630s. It explains that analytic geometry uses algebraic equations to describe geometric shapes on a coordinate system. This allows geometric relationships to be represented by algebraic equations using techniques like slope, gradients, and intercepts. It also covers topics like the Cartesian plane, lines, perpendicular and parallel lines, and finding equations of lines.
Proving trigonometric identities
The document provides guidance on proving trigonometric identities by:
1) Working with one side of the identity at a time using algebraic manipulations and basic trigonometric identities until both sides are equal.
2) Examples are presented showing the step-by-step work for proving several identities including using quotient, reciprocal, and Pythagorean identities.
3) Tips are given for practicing proving identities including redoing examples without looking at the solutions and not getting discouraged if it takes multiple attempts.
(8) Lesson 7.3 - Similarity and Transformations
This document provides instruction and examples for determining congruence and similarity using transformations. It explains that two figures are similar if one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations. Examples show using transformations and writing side ratios to determine if figures are similar. The last example finds the dimensions of an image that is enlarged twice by different scale factors, showing the results are similar.
Similarity day 1 sss, sas, aa
The document contains information about using similarity postulates to determine if triangles are similar and find unknown side lengths. It provides examples of using the AA, SAS, and SSS similarity postulates to show triangles are similar. It also shows using proportional sides to find missing lengths. The objective is for students to use similarity postulates to decide if triangles are similar and find unknowns.
Recommended
(8) Lesson 7.1 - Congruence and Transformations
1) The document discusses determining the coordinates of vertices after a dilation and provides examples. It also discusses congruence and using transformations like rotations, reflections, and translations to determine if two figures are congruent.
2) To determine congruence, you can use transformations to map one figure onto another. If a single or series of transformations can map all points of one figure directly onto the other, they are congruent.
3) Reflections, rotations, and translations will produce congruent figures as they preserve size and shape but change position.
Trigonometric Identities.
The document discusses three main groups of trigonometric identities: reciprocal relations which relate trig functions that are inverse of each other like tangent and cotangent; quotient relations which show relationships between ratios of trig functions like tangent being equal to the sine over the cosine; and the Pythagorean relation which is the fundamental relationship between sine and cosine where the square of one added to the square of the other is equal to 1. Examples are provided for each type of identity and an activity is included to practice using and filling in identity formulas.
6.6 proportions & similar triangles
This document discusses proportionality theorems and using similar triangles to solve problems involving segment lengths. It provides 6 theorems regarding proportional line segments in triangles and parallel lines cut by transversals. Examples are given to demonstrate using the theorems to find unknown segment lengths. Real-life applications involving building construction are also presented.
Triangle congruence
This document contains information about proving triangles congruent using various postulates and theorems of geometry including:
- SSS (side-side-side) postulate
- SAS (side-angle-side) postulate
- ASA (angle-side-angle) postulate
- AAS (angle-angle-side) theorem
- Hypotenuse-Leg theorem
It also defines key terms like hypotenuse and legs of a right triangle and presents the Pythagorean theorem.
Analytical geometry Grade 10
This document is a presentation on analytic geometry that was compiled from 6 different sources. It introduces analytic geometry and its history, developed by Descartes and Fermat in the 1630s. It explains that analytic geometry uses algebraic equations to describe geometric shapes on a coordinate system. This allows geometric relationships to be represented by algebraic equations using techniques like slope, gradients, and intercepts. It also covers topics like the Cartesian plane, lines, perpendicular and parallel lines, and finding equations of lines.
Proving trigonometric identities
The document provides guidance on proving trigonometric identities by:
1) Working with one side of the identity at a time using algebraic manipulations and basic trigonometric identities until both sides are equal.
2) Examples are presented showing the step-by-step work for proving several identities including using quotient, reciprocal, and Pythagorean identities.
3) Tips are given for practicing proving identities including redoing examples without looking at the solutions and not getting discouraged if it takes multiple attempts.
(8) Lesson 7.3 - Similarity and Transformations
This document provides instruction and examples for determining congruence and similarity using transformations. It explains that two figures are similar if one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations. Examples show using transformations and writing side ratios to determine if figures are similar. The last example finds the dimensions of an image that is enlarged twice by different scale factors, showing the results are similar.
Similarity day 1 sss, sas, aa
The document contains information about using similarity postulates to determine if triangles are similar and find unknown side lengths. It provides examples of using the AA, SAS, and SSS similarity postulates to show triangles are similar. It also shows using proportional sides to find missing lengths. The objective is for students to use similarity postulates to decide if triangles are similar and find unknowns.
Math 9 similar triangles intro
The document is a lecture on similar triangles. It defines similar triangles as having the same shape but different sizes, and discusses how similar triangles have corresponding angles that are congruent and corresponding sides that are proportional. It provides examples of similar triangles and statements showing their similarity. It also covers using proportions of corresponding sides to solve for missing sides in similar triangles and several proportionality principles related to similar triangles, including the basic proportionality theorem involving parallel lines cutting across a triangle.
Congruent figures
The document provides examples and explanations of congruent triangles. It begins with warm up questions about naming sides and angles of a triangle. It then discusses how to prove triangles are congruent using corresponding angles and sides being equal. Several examples are provided of using properties of congruent triangles to find missing angle measures or side lengths. Diagrams are included to illustrate bisectors and midpoints used in proofs of triangle congruence.
Trigonometric identities
This document discusses trigonometric functions and identities. It provides definitions of trig functions like sine, cosine, tangent, and cotangent. It then lists 8 fundamental trigonometric identities and the reciprocal, quotient, and Pythagorean relations between trig functions. It gives conditions and rules for transforming trig identities and examples of proving identities like secθ cotθ = cscθ and 2cos2θ - 1 = cos2θ−sin2θ. The document assigns proving additional identities like secѲ/cscѲ = tanѲ as homework.
DEFINED AND UNDEFINED TERMS IN GEOMETRY.pptx
This document appears to be a lesson plan on basic undefined and defined terms in geometry. The objectives are to:
1. Determine basic undefined terms like point, line, and plane and defined terms.
2. Name basic geometric figures appropriately.
3. Represent points, lines, and planes using models.
The lesson defines terms like point, line, plane and their representations. It discusses undefined terms like point, line, and plane and defined terms like collinear points and coplanar points. Examples and illustrations are provided to explain the concepts. Activities like naming figures and determining if statements are true or false are included for student practice.
Geometric Transformation: Rotation
Geometric Transformation. A geometric rotation refers to the rotating of a figure around a center of rotation.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Transformations in the coordinate plane
This document discusses four geometric transformations: translation, reflection, rotation, and dilation. It provides examples of each transformation in the coordinate plane and notes their unique properties. Translations, reflections, and rotations preserve both shape and size, creating congruent figures, while dilations preserve shape but change size, creating similar figures. The document also discusses using transformations to transform figures step-by-step in the coordinate plane.
1 3 points, lines, planes
This document defines key geometric concepts including points, lines, planes and their relationships. It explains that points have no size, lines extend indefinitely and planes are flat surfaces that extend without limits. It also covers topics like collinear points that lie on the same line, determining if objects are coplanar by lying on the same plane, and the different types of intersections between lines and planes, which can be a point, line or no intersection.
Related rates ppt
1. Related rates problems involve differentiating equations with respect to time to determine an unknown rate of change.
2. The general procedure is to define variables, write an equation relating the variables, implicitly differentiate with respect to time, and substitute known values and rates of change to solve for the unknown rate.
3. Examples include finding the rate of change of total area of a spreading pond ripple or the rate of change of radius of a inflating balloon given the rate air is being pumped in.
Proving Triangles Congruent Sss, Sas Asa
This document discusses different ways to prove that two triangles are congruent, including the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS) congruence postulates. It provides examples of applying each postulate to determine if pairs of triangles are congruent or not. There is no side-side-angle (SSA) or angle-angle-angle (AAA) postulate that can prove congruence.
Trigonometry Functions
This document provides an overview of trigonometric functions. It covers angles and their measurement in degrees and radians. It then discusses right triangle trigonometry, defining the six trigonometric functions and properties like fundamental identities. Special angle values are computed for 30, 45, and 60 degrees. Trig functions of general angles and the unit circle approach are introduced. Graphs of sine, cosine, tangent, cotangent, cosecant and secant functions are examined.
Basic proportionality theorem
The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides at distinct points, the lengths of the segments of the two sides will be divided in the same ratio. The proof involves drawing additional lines perpendicular to the parallel line and original sides of the triangle, allowing the areas of different triangles to be set equal and proving that the ratios of the corresponding segments are equal.
Taxicab Geometry Presentation
Tyler Roell presentation on Taxicab Geometry given at Franklin College High School Math Day, November 2009. Culmination of his MAT 490 (Individualized Study) project with Prof. Robert Talbert.
Congruent triangles
The document discusses various properties and theorems related to triangles. It begins by defining different types of triangles based on side lengths and angle measures. It then covers the four congruence rules for triangles: SAS, ASA, AAS, and SSS. The document proceeds to prove several theorems about relationships between sides and angles of triangles, such as opposite sides/angles of isosceles triangles being equal, larger sides having greater opposite angles, and the sum of any two angles being greater than the third side. It concludes by proving that the perpendicular from a point to a line is the shortest segment.
Factoring by grouping
How to factor by grouping
Assessments and examples are available
Can be used by a math teacher in her discussion about factoring
ASA, SAS,AAS,SSS
This document discusses triangle congruence, including definitions of triangles, corresponding sides and angles, and the four main postulates used to prove triangles are congruent: SSS, SAS, ASA, and SAA. It provides examples of determining if triangles are congruent and finding missing side lengths through algebraic applications of the congruence postulates and theorems. Key ideas covered are the properties of triangles, corresponding parts of congruent triangles, and using congruence rules to solve problems.
Algebraic functions powerpoint
This document defines and provides examples of algebraic functions. It explains that algebraic functions involve algebraic operations like addition, subtraction, multiplication, and division on variables and constants. It also discusses linear algebraic functions, which can be represented by a straight line on the Cartesian plane in the form of f(x)=mx+b. The document provides examples of linear functions using tables, graphs, and solving linear equations for y. It compares linear and quadratic functions, noting that while linear functions can be written as fractions, quadratic functions involve squared variables and are not linear.
GRADE 8-ILLUSTRATING THE SAS, ASA AND SSS.pptx
This document provides instruction on identifying included angles and sides of triangles and using the triangle congruence postulates SSS, SAS, and ASA. It contains examples of naming included angles when given two sides of a triangle and included sides when given two angles of a triangle. The three congruence postulates - side-side-side, side-angle-side, and angle-side-angle - are defined as well as examples of how to use each one to prove triangles are congruent. The document concludes with practice problems asking the reader to identify the missing part needed to prove triangles congruent using the postulates.
Module 2 similarity
This document provides information about Module 17 on similar triangles. The key points covered are:
1. The module discusses the definition of similar triangles, similarity theorems, and how to determine if two triangles are similar or find missing lengths using properties of similar triangles.
2. Students are expected to learn how to apply the definition of similar triangles, verify the AAA, SAS, and SSS similarity theorems, and use proportionality theorems to calculate lengths of line segments.
3. Several examples and exercises are provided to help students practice determining if triangles are similar, citing the appropriate similarity theorem, finding missing lengths, and applying properties of similar triangles.
Week 2 -Trapezoid and Kite.pptx
This lesson covers properties of trapezoids and kites. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and defines properties including that the nonparallel sides are legs and the parallel sides are bases. An isosceles trapezoid has congruent legs. The lesson also defines a kite as a quadrilateral with two pairs of consecutive congruent sides, and defines properties such as perpendicular diagonals and congruent non-vertex angles. Examples of solving problems involving finding angle measures of trapezoids and kites are provided.
Congruent Triangles
This document provides an overview of congruent triangles and the different rules that can be used to prove triangles are congruent. It defines congruent triangles as triangles that have the same size and shape. It then presents four main rules for proving triangles are congruent: 1) three sides are equal (SSS rule), 2) two sides and the included angle are equal (SAS rule), 3) two angles and a non-included side are equal (AAS rule), and 4) a right angle, hypotenuse, and one other side are equal (RHS rule). The document explains each rule and provides examples of how to apply them to identify matching elements and prove triangles congruent.
Chapter 7
The document provides examples and step-by-step explanations for solving geometry problems involving similar and congruent shapes using transformations and properties of similarity and congruence. In one example, it is determined that two triangles are similar because corresponding angles are congruent. In another example, transformations of a rotation and translation are used to show that two figures are congruent.
Lesson 7.2
This document contains a lesson on determining congruence between figures using transformations. It provides examples of identifying congruent triangles and determining the transformations needed to map one onto the other. It also gives examples of using congruence to find missing angle measures. The lesson explains that two figures are congruent if their corresponding sides are congruent and corresponding angles are congruent.
More Related Content
What's hot
Math 9 similar triangles intro
The document is a lecture on similar triangles. It defines similar triangles as having the same shape but different sizes, and discusses how similar triangles have corresponding angles that are congruent and corresponding sides that are proportional. It provides examples of similar triangles and statements showing their similarity. It also covers using proportions of corresponding sides to solve for missing sides in similar triangles and several proportionality principles related to similar triangles, including the basic proportionality theorem involving parallel lines cutting across a triangle.
Congruent figures
The document provides examples and explanations of congruent triangles. It begins with warm up questions about naming sides and angles of a triangle. It then discusses how to prove triangles are congruent using corresponding angles and sides being equal. Several examples are provided of using properties of congruent triangles to find missing angle measures or side lengths. Diagrams are included to illustrate bisectors and midpoints used in proofs of triangle congruence.
Trigonometric identities
This document discusses trigonometric functions and identities. It provides definitions of trig functions like sine, cosine, tangent, and cotangent. It then lists 8 fundamental trigonometric identities and the reciprocal, quotient, and Pythagorean relations between trig functions. It gives conditions and rules for transforming trig identities and examples of proving identities like secθ cotθ = cscθ and 2cos2θ - 1 = cos2θ−sin2θ. The document assigns proving additional identities like secѲ/cscѲ = tanѲ as homework.
DEFINED AND UNDEFINED TERMS IN GEOMETRY.pptx
This document appears to be a lesson plan on basic undefined and defined terms in geometry. The objectives are to:
1. Determine basic undefined terms like point, line, and plane and defined terms.
2. Name basic geometric figures appropriately.
3. Represent points, lines, and planes using models.
The lesson defines terms like point, line, plane and their representations. It discusses undefined terms like point, line, and plane and defined terms like collinear points and coplanar points. Examples and illustrations are provided to explain the concepts. Activities like naming figures and determining if statements are true or false are included for student practice.
Geometric Transformation: Rotation
Geometric Transformation. A geometric rotation refers to the rotating of a figure around a center of rotation.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
Transformations in the coordinate plane
This document discusses four geometric transformations: translation, reflection, rotation, and dilation. It provides examples of each transformation in the coordinate plane and notes their unique properties. Translations, reflections, and rotations preserve both shape and size, creating congruent figures, while dilations preserve shape but change size, creating similar figures. The document also discusses using transformations to transform figures step-by-step in the coordinate plane.
1 3 points, lines, planes
This document defines key geometric concepts including points, lines, planes and their relationships. It explains that points have no size, lines extend indefinitely and planes are flat surfaces that extend without limits. It also covers topics like collinear points that lie on the same line, determining if objects are coplanar by lying on the same plane, and the different types of intersections between lines and planes, which can be a point, line or no intersection.
Related rates ppt
1. Related rates problems involve differentiating equations with respect to time to determine an unknown rate of change.
2. The general procedure is to define variables, write an equation relating the variables, implicitly differentiate with respect to time, and substitute known values and rates of change to solve for the unknown rate.
3. Examples include finding the rate of change of total area of a spreading pond ripple or the rate of change of radius of a inflating balloon given the rate air is being pumped in.
Proving Triangles Congruent Sss, Sas Asa
This document discusses different ways to prove that two triangles are congruent, including the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS) congruence postulates. It provides examples of applying each postulate to determine if pairs of triangles are congruent or not. There is no side-side-angle (SSA) or angle-angle-angle (AAA) postulate that can prove congruence.
Trigonometry Functions
This document provides an overview of trigonometric functions. It covers angles and their measurement in degrees and radians. It then discusses right triangle trigonometry, defining the six trigonometric functions and properties like fundamental identities. Special angle values are computed for 30, 45, and 60 degrees. Trig functions of general angles and the unit circle approach are introduced. Graphs of sine, cosine, tangent, cotangent, cosecant and secant functions are examined.
Basic proportionality theorem
The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides at distinct points, the lengths of the segments of the two sides will be divided in the same ratio. The proof involves drawing additional lines perpendicular to the parallel line and original sides of the triangle, allowing the areas of different triangles to be set equal and proving that the ratios of the corresponding segments are equal.
Taxicab Geometry Presentation
Tyler Roell presentation on Taxicab Geometry given at Franklin College High School Math Day, November 2009. Culmination of his MAT 490 (Individualized Study) project with Prof. Robert Talbert.
Congruent triangles
The document discusses various properties and theorems related to triangles. It begins by defining different types of triangles based on side lengths and angle measures. It then covers the four congruence rules for triangles: SAS, ASA, AAS, and SSS. The document proceeds to prove several theorems about relationships between sides and angles of triangles, such as opposite sides/angles of isosceles triangles being equal, larger sides having greater opposite angles, and the sum of any two angles being greater than the third side. It concludes by proving that the perpendicular from a point to a line is the shortest segment.
Factoring by grouping
How to factor by grouping
Assessments and examples are available
Can be used by a math teacher in her discussion about factoring
ASA, SAS,AAS,SSS
This document discusses triangle congruence, including definitions of triangles, corresponding sides and angles, and the four main postulates used to prove triangles are congruent: SSS, SAS, ASA, and SAA. It provides examples of determining if triangles are congruent and finding missing side lengths through algebraic applications of the congruence postulates and theorems. Key ideas covered are the properties of triangles, corresponding parts of congruent triangles, and using congruence rules to solve problems.
Algebraic functions powerpoint
This document defines and provides examples of algebraic functions. It explains that algebraic functions involve algebraic operations like addition, subtraction, multiplication, and division on variables and constants. It also discusses linear algebraic functions, which can be represented by a straight line on the Cartesian plane in the form of f(x)=mx+b. The document provides examples of linear functions using tables, graphs, and solving linear equations for y. It compares linear and quadratic functions, noting that while linear functions can be written as fractions, quadratic functions involve squared variables and are not linear.
GRADE 8-ILLUSTRATING THE SAS, ASA AND SSS.pptx
This document provides instruction on identifying included angles and sides of triangles and using the triangle congruence postulates SSS, SAS, and ASA. It contains examples of naming included angles when given two sides of a triangle and included sides when given two angles of a triangle. The three congruence postulates - side-side-side, side-angle-side, and angle-side-angle - are defined as well as examples of how to use each one to prove triangles are congruent. The document concludes with practice problems asking the reader to identify the missing part needed to prove triangles congruent using the postulates.
Module 2 similarity
This document provides information about Module 17 on similar triangles. The key points covered are:
1. The module discusses the definition of similar triangles, similarity theorems, and how to determine if two triangles are similar or find missing lengths using properties of similar triangles.
2. Students are expected to learn how to apply the definition of similar triangles, verify the AAA, SAS, and SSS similarity theorems, and use proportionality theorems to calculate lengths of line segments.
3. Several examples and exercises are provided to help students practice determining if triangles are similar, citing the appropriate similarity theorem, finding missing lengths, and applying properties of similar triangles.
Week 2 -Trapezoid and Kite.pptx
This lesson covers properties of trapezoids and kites. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and defines properties including that the nonparallel sides are legs and the parallel sides are bases. An isosceles trapezoid has congruent legs. The lesson also defines a kite as a quadrilateral with two pairs of consecutive congruent sides, and defines properties such as perpendicular diagonals and congruent non-vertex angles. Examples of solving problems involving finding angle measures of trapezoids and kites are provided.
Congruent Triangles
This document provides an overview of congruent triangles and the different rules that can be used to prove triangles are congruent. It defines congruent triangles as triangles that have the same size and shape. It then presents four main rules for proving triangles are congruent: 1) three sides are equal (SSS rule), 2) two sides and the included angle are equal (SAS rule), 3) two angles and a non-included side are equal (AAS rule), and 4) a right angle, hypotenuse, and one other side are equal (RHS rule). The document explains each rule and provides examples of how to apply them to identify matching elements and prove triangles congruent.
What's hot (20)
Similar to (8) Lesson 7.4 - Properties of Similar Polygons
Chapter 7
The document provides examples and step-by-step explanations for solving geometry problems involving similar and congruent shapes using transformations and properties of similarity and congruence. In one example, it is determined that two triangles are similar because corresponding angles are congruent. In another example, transformations of a rotation and translation are used to show that two figures are congruent.
Lesson 7.2
This document contains a lesson on determining congruence between figures using transformations. It provides examples of identifying congruent triangles and determining the transformations needed to map one onto the other. It also gives examples of using congruence to find missing angle measures. The lesson explains that two figures are congruent if their corresponding sides are congruent and corresponding angles are congruent.
(8) Lesson 7.2 - Congruence
This document contains a lesson on determining congruence between figures using transformations. It provides examples of identifying congruent triangles and determining the transformations needed to map one onto the other. It also gives examples of using congruence to find missing angle measures. The lesson explains that two figures are congruent if their corresponding sides are congruent and corresponding angles are congruent.
J9 b06dbd
This document provides information about similar and congruent figures in geometry. It defines similar figures as those that have the same shape but not necessarily the same size, while congruent figures have both the same shape and the same size. Corresponding parts of similar figures, such as corresponding angles and sides, are identified and their properties are described. Examples are provided to demonstrate how to determine if figures are similar based on ratios of corresponding side lengths. Congruent figures are also discussed, noting that corresponding angles and sides of congruent figures are congruent. The document concludes with practice problems applying the concepts of similar and congruent figures.
Pandit Geometry Unit 3-lesson 06 and 09
This geometry lesson covers similarity and transformations. It begins with a warm-up activity identifying errors in a dilation. Students then sort transformation cards and write sequences of transformations. They practice identifying similar triangles using the Angle-Angle Similarity Theorem. The lesson emphasizes that similar figures have a sequence of rigid motions and dilations that map one onto the other. It introduces the definition of similarity and provides examples proving triangles similar based on angle and side relationships.
Unit 1. day 17 studyguide1
This document contains various sections on geometry topics including working warm-up problems about writing equations involving angle pairs formed by parallel lines cut by a transversal. It also lists common core standards about transformations of geometric figures and using properties of parallel lines cut by transversals to establish facts about angles. Finally, it reminds students that their exam is on Thursday and includes a study guide they should complete without talking.
Unit 1. day 15.quiz
This document contains information about angles and geometry concepts including:
1) Common Core standards related to congruence, similarity, rotations, reflections, and translations of geometric figures.
2) Questions about the definitions of vertical angles, corresponding angles, and supplementary angles.
3) A diagram labeling different angles and instructions for students to complete an assessment on related geometry topics.
Text 10.5 similar congruent polygons
Two polygons are similar if they have the same shape but not necessarily the same size. Congruent polygons have the same shape and the same size. The document provides examples of finding corresponding sides and angles of similar and congruent polygons. It also gives examples of determining if two polygons are similar by checking if the ratios of corresponding sides are equal.
parallelogram.pdf
The document is a rubric for assessing student work on a multi-part math task involving measurement of a parallelogram. It analyzes common student misunderstandings and errors, such as not including units, using incorrect area formulas, drawing triangles that are not right, and making claims without justification. The rubric evaluates students' ability to measure, calculate areas and perimeters, develop logical arguments comparing shapes, and represent geometric relationships algebraically. Most students struggled with conceptualizing height versus side length and applying measurement concepts rigorously.
Geometry unit 7.2
This document is about similarity and similar polygons from a Holt Geometry textbook. It defines similar polygons as polygons with congruent angles and proportional side lengths. Examples are provided to identify similar polygons and write similarity statements. The similarity ratio of two similar polygons is defined as the ratio of corresponding side lengths. Applications include using proportions to find the length of a model based on its similarity to an actual object.
Unit 1. day 11b
This document provides information about similar and congruent figures including:
1) Definitions of corresponding sides and angles, congruent figures, and similar figures. Similar figures have the same shape but not necessarily the same size, while congruent figures have the same size and shape.
2) Examples are given to identify the scale factor of similar figures as the ratio of corresponding sides.
3) Worked examples ask students to identify corresponding sides and angles of similar triangles, and use scale factors to find missing side lengths.
4) A closing asks students to share answers and discuss as needed.
SIMILARITY OF TRIANGLES.pptx
The document discusses similarity of triangles and geometric figures, noting that two figures are similar if they have the same shape but not necessarily the same size, and outlining the AA, SAS, SSS, and right triangle similarity theorems. It also reviews ratios, proportions, and how proportions can be used to show that corresponding segments of similar figures are proportional. The learning objectives are to illustrate similarity of figures and prove the conditions for similarity of triangles using these various theorems.
Theorems invloving inequalities in a triangle
This lesson plan is about The two theorems which involve Inequalities in a Triangle. Download it. it is useful
THE MIDLINE THEOREM-.pptx GRADE 9 MATHEMATICS THIRD QUARTER
1. The document discusses classroom rules which include listening when others are speaking, raising your hand to speak or get up, and being respectful.
2. It then provides an example of using the midline theorem to solve several geometry problems involving triangles. The midline theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
3. Finally, it discusses how the midline theorem can be applied in real life contexts like architecture and engineering for structures like rooftops, bridges, and buildings.
LET’S DO MATH.pptx
This document discusses geometry concepts like congruence, triangles, and their properties. It contains examples of:
- Using tangram pieces to complete a puzzle based on congruent shapes
- How congruence is used in mass production by ensuring identical copies are made
- Properties of triangle congruence like the reflexive, symmetric, and transitive properties
- Identifying sides, angles, and vertices of triangles in examples
- Defining terms and listing properties of congruence
The document provides instruction and activities to help students learn about geometric concepts like congruence through examples, definitions, and identifying parts of shapes.
Lesson 7.3 (8)
This document provides instruction and examples for determining congruence and similarity using transformations. It explains that two figures are similar if one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations. Examples show using transformations and writing side ratios to determine if figures are similar. The last example finds the dimensions of an image that is enlarged twice by different scale factors, showing the results are similar.
DLL3 MATH 9 WEEK 7.docx
This document is a daily lesson log for a 9th grade mathematics class taught by Angela Camille P. Cariaga from April 3-7, 2023. The lesson focused on the key concepts of quadrilaterals and triangle similarity. Students learned to investigate, analyze, and solve problems involving quadrilaterals and triangle similarity. Throughout the week, students illustrated similarity of figures, reviewed and continued learning about similarity of polygons and figures, and took a quiz. Activities included observing similar figures, solving proportions, drawing similar shapes, and identifying examples of similarity in daily life. The lesson aimed to help students understand that two polygons are similar if their corresponding angles are congruent and corresponding sides are proportional.
RO Q3 M4 MATH9 pdf.pdf
This document contains a mathematics lesson on solving word problems involving parallelograms, trapezoids, and kites. It begins with an introduction to the key properties of parallelograms, trapezoids, and kites. It then provides 4 examples of word problems involving these shapes and shows the step-by-step work and reasoning to solve each problem using the relevant geometric properties. The lesson aims to teach students how to illustrate, set up, and solve word problems involving parallelograms, trapezoids, and kites.
SBTP - Activity sheet for proving law of sines and cosines DavNor Div
This document provides an activity sheet to teach students how to solve for unknown parts of an oblique triangle. It introduces an oblique triangle ABC with sides of length a, b, c and altitude h. Students are asked to derive equations relating the sides and angles using properties of trigonometry and similar triangles. These include deriving one of the Law of Cosines formulas by relating b^2 to h^2 and x^2, then substituting x in terms of b and angle A. Students are also asked to derive the other two Law of Cosines formulas and the Law of Sines by drawing additional altitudes and writing proportional relationships between sides and opposite angles.
(8) Lesson 3.1
Here are some real-world examples of relationships that have a constant rate of change:
- The speed of a car traveling at a constant velocity - As time passes, the car's position changes at a steady rate.
- Interest accumulating in a bank account - The interest earned each time period is a constant percentage of the current balance.
- Population growth over time - If the birth and death rates remain steady, the population will increase at a constant percentage each year.
- Depreciation of an asset - Most assets lose value at a steady rate each year due to age and wear.
- Temperature change from heating or cooling an object - The temperature will change at a steady rate until the object reaches equilibrium with its
Similar to (8) Lesson 7.4 - Properties of Similar Polygons (20)
THE MIDLINE THEOREM-.pptx GRADE 9 MATHEMATICS THIRD QUARTER
THE MIDLINE THEOREM-.pptx GRADE 9 MATHEMATICS THIRD QUARTER
SBTP - Activity sheet for proving law of sines and cosines DavNor Div
SBTP - Activity sheet for proving law of sines and cosines DavNor Div
More from wzuri
Chapter 3
- Mauldin Middle School wants to make $4,740 from yearbook sales. Print yearbooks cost $60 each and digital yearbooks cost $15 each.
- This relationship can be represented by the equation 60x + 15y = 4,740.
- Setting y = 0 in the equation yields an x-intercept of 79, meaning 79 print yearbooks would earn the school $4,740.
- Setting x = 0 yields a y-intercept of 316, meaning 316 digital yearbooks would earn the school $4,740.
Chapter 2 inquiry_lab_presentation_course_3 (1)
A bar diagram helps solve a two-step equation problem by visually representing the quantities and their relationships. The bar diagram shows the total number of postcards Miranda bought and the total cost. It can be used to write an equation relating the unknown cost of a large postcard to the total quantity and cost. Solving this equation reveals that the cost of one large postcard is $2.50.
Chapter 2 Review
This document discusses equivalence and solving equations. It begins with defining equivalence as the product of a number and its multiplicative inverse being 1. It then provides examples of solving various equations using properties of equality like addition, subtraction, multiplication and division. These include one-step, two-step and multi-step equations with or without variables on both sides. It also discusses equations having no solutions, one solution, or infinitely many solutions.
Chapter 2 lesson_4_presentation_course_3
The document provides examples for solving linear equations using the work backward strategy. It includes 4 example equations with the step-by-step work shown. The answers are then provided. Additional material is included on equivalence, solving equations with variables on both sides, and using properties of equality.
Chapter 5
This document provides examples and explanations for using algebraic concepts in geometry, specifically regarding angles formed when lines are cut by a transversal. It defines key terms like parallel lines, transversal, interior angles, exterior angles, alternate interior angles, alternate exterior angles, and corresponding angles. Examples are given to classify pairs of angles and find missing angle measures. Step-by-step examples walk through using properties of parallel lines cut by a transversal to find missing angles. The document also explains how to prove conjectures using paragraph and two-column proofs.
Lesson 5.1
This document discusses classifying angles formed when parallel lines are cut by a transversal. It defines key terms like alternate interior angles, alternate exterior angles, and corresponding angles. It then provides examples of classifying angle pairs based on their relationship. Sample problems are worked through, applying the concepts to find missing angle measures by justifying answers using angle properties of parallel lines cut by a transversal.
Lesson 1.8 grade 8
1. The document provides examples for evaluating expressions with scientific notation, square roots, and cube roots. It includes step-by-step workings for finding square roots of perfect squares and cube roots of perfect cubes.
2. Key concepts explained are square roots, perfect squares, radical signs, cube roots, and perfect cubes. Examples are provided to find square roots of numbers less than 100 and cube roots of small numbers.
3. Knowing how to find the exact square roots of perfect squares helps estimate the square roots of nearby non-perfect squares. Being able to write the perfect square root without the radical provides understanding and allows for computations.
Lesson 7.4
This document provides instruction on determining if two figures are similar using transformations. It includes examples of determining if figures are similar by checking if corresponding angles are congruent and if corresponding sides are proportional. It also covers finding missing measures in similar figures using scale factors and proportions. Determining similarity involves rotations, reflections, translations, and dilations, while congruence only involves rigid motions.
Pat05 ppt 0201
This document provides an overview of functions and concepts covered in Chapter 2, including:
- Graphing functions to identify intervals where they are increasing, decreasing, or constant.
- Modeling real-world applications with appropriate functions.
- Graphing functions defined piecewise using different formulas for different parts of the domain.
- Identifying relative maximum and minimum values of functions.
- Defining functions as increasing, decreasing, or constant on intervals.
- Describing the greatest integer function.
Chapter 6
This document provides examples and explanations for describing geometric transformations on a coordinate plane, including translations, reflections, rotations, and dilations. It defines key terms like preimage, image, and scale factor. Examples show how to perform and describe each type of transformation by:
1) Graphing a figure and identifying its vertices with coordinates
2) Performing the transformation by applying the rules for that specific transformation
3) Graphing the transformed image and identifying the new coordinates of its vertices
The document ensures understanding through multiple examples of each transformation type and encourages practicing the skills on additional example problems. It emphasizes that transformations preserve properties like distance and angle measures.
Pat05 ppt 0106
This document discusses solving linear inequalities and compound inequalities. It provides examples of solving various inequalities algebraically and graphing their solution sets. It also gives an example of setting up and solving an inequality to model a real-world situation about payment plans for a house painting job.
Pat05 ppt 0105
This document discusses linear equations and functions. It provides examples of solving linear equations, including special cases where equations have no solution or infinitely many solutions. Applications involving linear models for distance, rate, and time as well as simple interest are presented. The key concepts of zeros of linear functions and finding the zero of a given linear function are also covered.
Chapter 1 Review
- To write fractions as decimals and decimals as fractions, it is helpful to write numbers in different ways. This allows for easier comparisons and calculations.
- Rational numbers can be written as ratios of integers, repeating decimals can be written as fractions, and terminating decimals can be written as fractions.
- Writing numbers in different forms, such as fractions and decimals, allows for easier evaluation of expressions and calculations.
Lesson 1.10 grade 8
This document provides examples and explanations of concepts related to classifying and ordering different types of numbers:
1) It defines rational and irrational numbers, and provides examples of each. Rational numbers can be expressed as ratios of integers, while irrational numbers cannot.
2) Exercises are included for classifying numbers as rational or irrational, comparing irrational numbers on a number line, and ordering sets of numbers from least to greatest.
3) Answering "Why is it helpful to write numbers in different ways?" the document explains that not all numbers can be written the same way, like irrational numbers that cannot be expressed as integers. Being able to classify numbers facilitates understanding and operations involving different types of numbers.
Lesson 1.9 grade 8
This document provides examples for estimating square roots and cube roots of numbers that are not perfect squares or cubes. It shows how to estimate the value by finding the largest perfect square or cube below the number and the smallest perfect square or cube above it. The square or cube roots of these numbers are then used to determine an integer estimate between them. Several step-by-step examples are provided to demonstrate this process. Common Core State Standards addressed in the lesson are also listed.
Lesson 1.7 grade 8
1. The document provides examples of writing numbers in standard form and scientific notation. It also gives examples of performing arithmetic operations such as addition, subtraction, multiplication, and division on numbers expressed in scientific notation.
2. The examples calculate population sizes, planet diameters, and perform other calculations to illustrate how scientific notation makes working with very large and small numbers easier.
3. Writing numbers in scientific notation allows for easier operations like multiplication and division of very large and small quantities, as well as comparing the relative sizes of numbers like population and distances in the solar system.
Lesson 1.7 grade 8
1) The document provides examples of writing numbers in standard form and scientific notation. It also gives examples of performing arithmetic operations such as addition, subtraction, multiplication, and division on numbers expressed in scientific notation.
2) The examples illustrate how writing very large or very small numbers in scientific notation makes it easier to perform operations with them. It also allows for estimating quantities that would otherwise be difficult to comprehend in standard form.
3) Understanding scientific notation helps to compare quantities that differ vastly in magnitude, such as populations and diameters of astronomical objects. It enables estimating ratios and relative sizes in a straightforward manner.
Lesson 1.6 (8)
Here are the steps to write a number between 0 and 1 in scientific notation with an example:
1. Write the number in decimal form. For example, 0.000375.
2. Count the number of decimal places in the number. In this example there are 4 decimal places.
3. Move the decimal point to the left by that number of places. This gives 3.75.
4. Write the number as a coefficient and exponent of 10. Since we moved the decimal point 4 places to the left, the exponent is -4.
So, 0.000375 written in scientific notation is 3.75 × 10-4.
Lesson 1.5 (8)
This document provides examples for writing numbers using negative exponents. It begins with examples of writing expressions like 6-3 and 4-4 using positive exponents. It then provides step-by-step examples of writing fractions with negative exponents other than -1, like writing 5-2. Further examples show simplifying expressions using the properties of exponents, like 53 • 5-5 = 53 + (-5). In the examples, writing numbers with negative exponents allows writing very small or large numbers without fractions and makes multiplying or dividing numbers with the same base easier.
Lesson 1.4 (8)
1. This document provides examples and explanations for simplifying expressions using exponents. It discusses the laws for taking the power of a power and the power of a product.
2. For the power of a power, you multiply the exponents. For the power of a product, you find the power of each factor and multiply them.
3. Several multi-step examples are worked through applying these laws to simplify expressions with variables and integers. The document also provides explanations of how rewriting numbers with exponents can make calculations easier.
More from wzuri (20)
Recently uploaded
How to deliver Powerpoint Presentations.pptx
"How to make and deliver dynamic presentations by making it more interactive to captivate your audience attention"
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaHow to Make a Field Mandatory in Odoo 17
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcPCOS corelations and management through Ayurveda.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneYour Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.Recently uploaded (20)
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
(8) Lesson 7.4 - Properties of Similar Polygons
- 1. Course 3, Lesson 7-4 Determine if the two figures are similar by using transformations. Explain your reasoning. 1. 2. 3. What type of transformation produces a figure that is not congruent to the original figure?
- 2. Course 3, Lesson 7-4 ANSWERS 1. yes; Sample answer: A dilation and a translation maps figure MNOP onto figure ABCD. 2. no; Sample answer: The ratio of the side lengths are not equal. 3. dilation
- 3. HOW can you determine congruence and similarity? Geometry Course 3, Lesson 7-4
- 4. Course 3, Lesson 7-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. • 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. Geometry
- 5. To • use corresponding angles and sides to determine similarity, • find missing measures in two similar figures Course 3, Lesson 7-4 Geometry
- 6. • similar polygons • scale factor Symbols • is similar to Course 3, Lesson 7-4 Geometry
- 7. Course 3, Lesson 7-4 Geometry Words If two polygons are similar, then • their corresponding angles are congruent and • the measures of their corresponding sides are proportional. Model Symbols , , , AB BC AC A X B Y C Z XY YZ XZ and
- 8. 1 Need Another Example? 2 3 Step-by-Step Example 1. Determine whether rectangle HJKL is similar to rectangle MNPQ. Explain. First, check to see if corresponding angles are congruent. Since the two polygons are rectangles, all of their angles are right angles. Therefore, all corresponding angles are congruent. Next, check to see if corresponding sides are proportional. Since and are not equivalent, the rectangles are not similar.
- 9. Answer Need Another Example? Determine whether triangle DEF is similar to triangle HJK. Explain. Yes; the corresponding angles are congruent and
- 10. 1 Need Another Example? 2 3 Step-by-Step Example 2. Quadrilateral WXYZ is similar to quadrilateral ABCD. a. Find the scale factor from quadrilateral ABCD to quadrilateral WXYZ. So, a length on polygon WXYZ is times as long as the corresponding length on polygon ABCD. Let m represent the measure of XY. Set up a proportion to find the missing measure. a. Describe the transformations that map WXYZ onto ABCD. b. Find the missing measure. Since the figures are similar, they are not the same size. Choose two corresponding sides and determine what transformations will map one onto the other. A translation followed by a dilation will map AB onto WX. b. scale factor: = or m = (12) Write the equation. Multiply. Write the proportion. XY = m, BC = 12, YZ = 15, CD = 10 Find the cross products. Simplify. Division Property of Equality m • 10 = 12 • 15 10m = 180 m = 18 m = 18
- 11. Answer Need Another Example? Rectangle LMNO is similar to rectangle GHIJ. a. Describe the transformations that map GHIJ onto LMNO. b. Find the missing measure. a. Since the figures are similar, they are not the same size. The transformation is a translation and a dilation. b. 6
- 12. How did what you learned today help you answer the HOW can you determine congruence and similarity? Course 3, Lesson 7-4 Geometry
- 13. How did what you learned today help you answer the HOW can you determine congruence and similarity? Course 3, Lesson 7-4 Geometry Sample answer: • If two polygons have corresponding angles that are congruent and corresponding sides that are proportional, then they are similar.
- 14. A rectangle has a length of 10 feet and a height of 12 feet. Another rectangle that is similar to the first has a length of 15 feet. What is the height of the second rectangle? Course 3, Lesson 7-4 Ratios and Proportional RelationshipsFunctionsGeometry