This is a review game for a teacher to use in a geometry class. It goes over relationships in triangles, including bisetors, medians, altitudes, and inequalities and triangles.
This document provides a lesson on indirect proofs and inequalities in one triangle from Holt Geometry. It includes examples of writing indirect proofs, ordering triangle side lengths and angle measures, applying the triangle inequality theorem, finding possible side lengths of a triangle, and using triangle inequalities in a travel application problem. Practice problems are provided to check understanding. The key concepts covered are indirect proof, triangle inequalities, and relating triangle side lengths to angle measures.
The document provides information about geometry, specifically angles of triangles. It discusses the triangle angle sum theorem, which states that the sum of the interior angles of any triangle is 180 degrees. It provides examples of using this theorem to find missing angle measures in triangles. It also covers exterior angles and their relationships to interior angles, including theorems such as the exterior angle theorem. The document aims to teach students about important angle properties and relationships in triangles through definitions, theorems, and worked examples.
This document discusses properties of triangles related to side lengths and angles. It states that if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side. It also states that if one angle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. The document then asks the reader to identify the longest and shortest sides of a triangle based on these properties.
The document discusses various theorems and properties related to triangles, including:
1) The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
2) The triangle inequality theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
3) Properties relating the lengths of sides and measures of angles in a triangle, such as if sides are unequal then angles will be unequal as well.
The document discusses inequalities between sides and angles of triangles. It states that if the measures of the sides of a triangle are unequal, then the measures of the angles opposite those sides are unequal in the same order (Theorem 7-6). Similarly, if the measures of the angles of a triangle are unequal, then the measures of the sides opposite those angles are unequal in the same order (Theorem 7-7). It also discusses the triangle inequality theorem, which states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
The document discusses the exterior angle theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the remote interior angles and is greater than either of the remote interior angles. It defines key terms such as exterior angle, interior angle, remote interior angle, and provides examples of applying the exterior angle theorem and exterior angle inequality theorem to solve problems about angle measures in triangles.
The document is a submission by King Evaggeleu P. Cabaguio to Ms. Lovely A. Rosales containing activities on triangles. The activities explore properties of triangles, including relationships between angle and side measures, forming triangles with given side lengths, comparing exterior and interior angles, and conjecturing triangle theorems. Students are asked to make observations and comparisons to develop understandings of triangle inequalities.
The document discusses several theorems related to triangles:
1) The triangle inequality theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than their difference.
2) The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the remote interior angles.
3) The hinge theorem states that if two triangles have two congruent sides but not congruent included angles, then the third sides will be unequal, with the longer side opposite the larger angle.
This document provides a lesson on indirect proofs and inequalities in one triangle from Holt Geometry. It includes examples of writing indirect proofs, ordering triangle side lengths and angle measures, applying the triangle inequality theorem, finding possible side lengths of a triangle, and using triangle inequalities in a travel application problem. Practice problems are provided to check understanding. The key concepts covered are indirect proof, triangle inequalities, and relating triangle side lengths to angle measures.
The document provides information about geometry, specifically angles of triangles. It discusses the triangle angle sum theorem, which states that the sum of the interior angles of any triangle is 180 degrees. It provides examples of using this theorem to find missing angle measures in triangles. It also covers exterior angles and their relationships to interior angles, including theorems such as the exterior angle theorem. The document aims to teach students about important angle properties and relationships in triangles through definitions, theorems, and worked examples.
This document discusses properties of triangles related to side lengths and angles. It states that if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side. It also states that if one angle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. The document then asks the reader to identify the longest and shortest sides of a triangle based on these properties.
The document discusses various theorems and properties related to triangles, including:
1) The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
2) The triangle inequality theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
3) Properties relating the lengths of sides and measures of angles in a triangle, such as if sides are unequal then angles will be unequal as well.
The document discusses inequalities between sides and angles of triangles. It states that if the measures of the sides of a triangle are unequal, then the measures of the angles opposite those sides are unequal in the same order (Theorem 7-6). Similarly, if the measures of the angles of a triangle are unequal, then the measures of the sides opposite those angles are unequal in the same order (Theorem 7-7). It also discusses the triangle inequality theorem, which states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
The document discusses the exterior angle theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the remote interior angles and is greater than either of the remote interior angles. It defines key terms such as exterior angle, interior angle, remote interior angle, and provides examples of applying the exterior angle theorem and exterior angle inequality theorem to solve problems about angle measures in triangles.
The document is a submission by King Evaggeleu P. Cabaguio to Ms. Lovely A. Rosales containing activities on triangles. The activities explore properties of triangles, including relationships between angle and side measures, forming triangles with given side lengths, comparing exterior and interior angles, and conjecturing triangle theorems. Students are asked to make observations and comparisons to develop understandings of triangle inequalities.
The document discusses several theorems related to triangles:
1) The triangle inequality theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than their difference.
2) The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the remote interior angles.
3) The hinge theorem states that if two triangles have two congruent sides but not congruent included angles, then the third sides will be unequal, with the longer side opposite the larger angle.
This document provides a tentative schedule for the content and exams in a Modern Geometry course. It outlines the chapters and topics to be covered over 15 weeks, including two-dimensional and three-dimensional shapes, perimeter, area, volume, logic and proofs of triangle congruence, parallel lines, similarity, right triangles, trigonometry, circles, arcs, chords, and secants. Recommended textbook problems are listed for each section. There are 4 exams scheduled to assess comprehension of the material as it is covered throughout the course.
This document discusses parallel lines and transversals. It defines key terms like corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. It presents theorems about angle relationships that are created when parallel lines are cut by a transversal, such as corresponding angles being congruent and consecutive interior angles being supplementary. Examples are provided to demonstrate applying these concepts and theorems to find missing angle measures. Students are assigned practice problems to reinforce their understanding of using parallel lines and transversals to solve for unknown angle measures.
The document discusses the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. It provides examples of lengths that can and cannot form a triangle based on this theorem. It also explains how to find the possible range of values for the third side of a triangle when given the lengths of two sides.
1) The document describes an activity where students measure angles and side lengths of triangles to determine relationships.
2) They find that when one angle is larger than another in a triangle, the side opposite the larger angle is longer.
3) The longest side of a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
This document provides examples and explanations for proving triangles similar using the Angle-Angle (AA) criterion. It includes examples of showing two triangles are similar by showing they have two pairs of congruent angles. It also includes examples of writing similarity statements and using proportions to find missing side lengths when corresponding angles and one pair of corresponding sides are given. Guided practice problems allow students to practice determining if triangles are similar and writing similarity statements.
This document provides an overview of triangles, including their properties, types, similarity, areas of similar triangles, and Pythagorean theorem. It defines triangles as polygons with three sides and angles, and notes the angle sum property. Triangles are classified by angle and side length into right, obtuse, acute, isosceles, equilateral, and scalene varieties. Similarity is discussed, along with criteria like equal angles and proportional sides. Areas of similar triangles are directly proportional to a scale factor. Finally, the Pythagorean theorem and its applications to find missing sides of right triangles are covered.
This document discusses parallel lines and transversals. It provides examples of using theorems about alternate interior angles, corresponding angles, vertical angles, and consecutive interior angles to solve for unknown angle measures. Theorems demonstrated include the alternate interior angles theorem, vertical angles congruence theorem, and consecutive interior angles theorem. Students are guided through practice problems applying these theorems to find missing angle measures given information about parallel lines cut by a transversal.
This document provides an introduction to coordinate geometry and the Cartesian coordinate system. It defines key terms like coordinates, quadrants, and plotting points. The Cartesian plane is formed by the intersection of the x and y axes, with the origin at (0,0). Any point can be uniquely identified using an ordered pair (x,y) representing the distances from the x and y axes. Examples are given of plotting points and calculating distances between points on the plane using their coordinates. In summary, the document outlines the basic concepts of the Cartesian coordinate system used in coordinate geometry.
1. The document discusses key concepts related to lines and angles in geometry including parallel lines, intersecting lines, angles, and properties of triangles.
2. It defines important terms like points, lines, rays, angles, and angle types. Theorems are presented about vertically opposite angles, angles formed by parallel lines and transversals, and the angle sum property of triangles.
3. Examples and exercises are provided to illustrate theorems about the sums of interior and exterior angles of triangles always equalling 180 degrees and properties of angles formed when parallel lines are intersected by a transversal line.
Similar figures are two figures that are the same shape but can differ in size. To be similar, the corresponding sides must be proportional, meaning they differ by a constant scale factor. The angles of similar figures will always be congruent since similarity preserves angles. Similarity can be used to solve real-world problems involving scale diagrams or finding unknown heights and distances.
There are four types of lines that can be drawn in a triangle:
1. A perpendicular bisector of a side bisects the side at a 90 degree angle.
2. An angle bisector bisects the interior angle of the triangle into two equal angles.
3. A height or altitude drops perpendicular from a vertex to the opposite side.
4. A median connects a vertex to the midpoint of the opposite side.
The document provides instructions for an activity where students work in groups to cut out triangles from shapes. They sort and group the triangles based on similar characteristics and compare corresponding angles and sides. Students then measure and record side lengths and angle measurements of triangles within each group. They are tasked with labeling additional similar triangles without tools based on given scale factors between pairs of triangles. The purpose is for students to observe properties of similar figures and learn related vocabulary terms like similar figures, corresponding angles and sides, and scale factor.
1. The document provides information and examples about geometry concepts including triangles, the Pythagorean theorem, area, perimeter, circles, surface area, and volume.
2. It explains key terms like radius, diameter, circumference, and formulas for finding the area of squares, rectangles, triangles, and circles.
3. Step-by-step examples are given for using formulas to calculate the area of shapes and the circumference of circles.
Strategic Intervention Material (SIM) Mathematics-TWO-COLUMN PROOFSophia Marie Verdeflor
The document provides instructions for writing two-column geometric proofs. It explains that a two-column proof consists of statements in the left column and reasons for those statements in the right column. Each step of the proof is a row. It then gives examples of properties that can be used as reasons, such as angle addition postulate, congruent supplements theorem, and triangle congruence postulates. Sample proofs are also provided to illustrate the two-column format.
The document is a series of math problems presented by Ms. Prue involving geometry theorems, trigonometric functions, and other concepts. The problems are arranged in a 5x5 grid and cover topics like the Pythagorean theorem, triangle congruence, inverse/contrapositive statements, and solving equations. The goal is to apply mathematical rules and reasoning to arrive at the correct solutions, definitions, or determinations for each problem.
- A triangle is a three-sided polygon with three angles that sum to 180 degrees. Triangles can be classified based on side length (scalene, isosceles, equilateral) or angle type (acute, right, obtuse).
- The triangle inequality theorem states that any side of a triangle must be less than the sum of the other two sides and greater than the difference of the other two sides.
- A quadrilateral is a four-sided polygon. Quadrilaterals can be simple or complex, and simple ones can be convex or concave. The interior angles of any simple quadrilateral sum to 360 degrees.
- A circle is the set of all points in a plane equid
SIM Angles Formed by Parallel Lines cut by a Transversalangelamorales78
The document discusses parallel lines cut by a transversal and the angle relationships that are formed. It defines parallel lines and transversals, and describes the different types of angles formed, including alternate interior angles, alternate exterior angles, corresponding angles, same side interior angles, and same side exterior angles. Examples are given to demonstrate finding missing angle measures using properties of parallel lines cut by a transversal.
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.
If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle. Similarly, if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. It can be written as inequalities comparing the different side lengths, such as AB + AC > BC. The converse is also true - the side opposite the largest angle will be the longest side. Examples demonstrate using the triangle inequality theorem to determine if a set of lengths could form a triangle or find the possible range of values for the third side of a triangle given two side lengths.
This document provides a tentative schedule for the content and exams in a Modern Geometry course. It outlines the chapters and topics to be covered over 15 weeks, including two-dimensional and three-dimensional shapes, perimeter, area, volume, logic and proofs of triangle congruence, parallel lines, similarity, right triangles, trigonometry, circles, arcs, chords, and secants. Recommended textbook problems are listed for each section. There are 4 exams scheduled to assess comprehension of the material as it is covered throughout the course.
This document discusses parallel lines and transversals. It defines key terms like corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. It presents theorems about angle relationships that are created when parallel lines are cut by a transversal, such as corresponding angles being congruent and consecutive interior angles being supplementary. Examples are provided to demonstrate applying these concepts and theorems to find missing angle measures. Students are assigned practice problems to reinforce their understanding of using parallel lines and transversals to solve for unknown angle measures.
The document discusses the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. It provides examples of lengths that can and cannot form a triangle based on this theorem. It also explains how to find the possible range of values for the third side of a triangle when given the lengths of two sides.
1) The document describes an activity where students measure angles and side lengths of triangles to determine relationships.
2) They find that when one angle is larger than another in a triangle, the side opposite the larger angle is longer.
3) The longest side of a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
This document provides examples and explanations for proving triangles similar using the Angle-Angle (AA) criterion. It includes examples of showing two triangles are similar by showing they have two pairs of congruent angles. It also includes examples of writing similarity statements and using proportions to find missing side lengths when corresponding angles and one pair of corresponding sides are given. Guided practice problems allow students to practice determining if triangles are similar and writing similarity statements.
This document provides an overview of triangles, including their properties, types, similarity, areas of similar triangles, and Pythagorean theorem. It defines triangles as polygons with three sides and angles, and notes the angle sum property. Triangles are classified by angle and side length into right, obtuse, acute, isosceles, equilateral, and scalene varieties. Similarity is discussed, along with criteria like equal angles and proportional sides. Areas of similar triangles are directly proportional to a scale factor. Finally, the Pythagorean theorem and its applications to find missing sides of right triangles are covered.
This document discusses parallel lines and transversals. It provides examples of using theorems about alternate interior angles, corresponding angles, vertical angles, and consecutive interior angles to solve for unknown angle measures. Theorems demonstrated include the alternate interior angles theorem, vertical angles congruence theorem, and consecutive interior angles theorem. Students are guided through practice problems applying these theorems to find missing angle measures given information about parallel lines cut by a transversal.
This document provides an introduction to coordinate geometry and the Cartesian coordinate system. It defines key terms like coordinates, quadrants, and plotting points. The Cartesian plane is formed by the intersection of the x and y axes, with the origin at (0,0). Any point can be uniquely identified using an ordered pair (x,y) representing the distances from the x and y axes. Examples are given of plotting points and calculating distances between points on the plane using their coordinates. In summary, the document outlines the basic concepts of the Cartesian coordinate system used in coordinate geometry.
1. The document discusses key concepts related to lines and angles in geometry including parallel lines, intersecting lines, angles, and properties of triangles.
2. It defines important terms like points, lines, rays, angles, and angle types. Theorems are presented about vertically opposite angles, angles formed by parallel lines and transversals, and the angle sum property of triangles.
3. Examples and exercises are provided to illustrate theorems about the sums of interior and exterior angles of triangles always equalling 180 degrees and properties of angles formed when parallel lines are intersected by a transversal line.
Similar figures are two figures that are the same shape but can differ in size. To be similar, the corresponding sides must be proportional, meaning they differ by a constant scale factor. The angles of similar figures will always be congruent since similarity preserves angles. Similarity can be used to solve real-world problems involving scale diagrams or finding unknown heights and distances.
There are four types of lines that can be drawn in a triangle:
1. A perpendicular bisector of a side bisects the side at a 90 degree angle.
2. An angle bisector bisects the interior angle of the triangle into two equal angles.
3. A height or altitude drops perpendicular from a vertex to the opposite side.
4. A median connects a vertex to the midpoint of the opposite side.
The document provides instructions for an activity where students work in groups to cut out triangles from shapes. They sort and group the triangles based on similar characteristics and compare corresponding angles and sides. Students then measure and record side lengths and angle measurements of triangles within each group. They are tasked with labeling additional similar triangles without tools based on given scale factors between pairs of triangles. The purpose is for students to observe properties of similar figures and learn related vocabulary terms like similar figures, corresponding angles and sides, and scale factor.
1. The document provides information and examples about geometry concepts including triangles, the Pythagorean theorem, area, perimeter, circles, surface area, and volume.
2. It explains key terms like radius, diameter, circumference, and formulas for finding the area of squares, rectangles, triangles, and circles.
3. Step-by-step examples are given for using formulas to calculate the area of shapes and the circumference of circles.
Strategic Intervention Material (SIM) Mathematics-TWO-COLUMN PROOFSophia Marie Verdeflor
The document provides instructions for writing two-column geometric proofs. It explains that a two-column proof consists of statements in the left column and reasons for those statements in the right column. Each step of the proof is a row. It then gives examples of properties that can be used as reasons, such as angle addition postulate, congruent supplements theorem, and triangle congruence postulates. Sample proofs are also provided to illustrate the two-column format.
The document is a series of math problems presented by Ms. Prue involving geometry theorems, trigonometric functions, and other concepts. The problems are arranged in a 5x5 grid and cover topics like the Pythagorean theorem, triangle congruence, inverse/contrapositive statements, and solving equations. The goal is to apply mathematical rules and reasoning to arrive at the correct solutions, definitions, or determinations for each problem.
- A triangle is a three-sided polygon with three angles that sum to 180 degrees. Triangles can be classified based on side length (scalene, isosceles, equilateral) or angle type (acute, right, obtuse).
- The triangle inequality theorem states that any side of a triangle must be less than the sum of the other two sides and greater than the difference of the other two sides.
- A quadrilateral is a four-sided polygon. Quadrilaterals can be simple or complex, and simple ones can be convex or concave. The interior angles of any simple quadrilateral sum to 360 degrees.
- A circle is the set of all points in a plane equid
SIM Angles Formed by Parallel Lines cut by a Transversalangelamorales78
The document discusses parallel lines cut by a transversal and the angle relationships that are formed. It defines parallel lines and transversals, and describes the different types of angles formed, including alternate interior angles, alternate exterior angles, corresponding angles, same side interior angles, and same side exterior angles. Examples are given to demonstrate finding missing angle measures using properties of parallel lines cut by a transversal.
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.
If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle. Similarly, if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. It can be written as inequalities comparing the different side lengths, such as AB + AC > BC. The converse is also true - the side opposite the largest angle will be the longest side. Examples demonstrate using the triangle inequality theorem to determine if a set of lengths could form a triangle or find the possible range of values for the third side of a triangle given two side lengths.
This document discusses triangle congruence using the ASA, AAS, and Hypotenuse-Leg (HL) theorems. It provides examples of applying these theorems to determine if triangles are congruent and to prove triangles congruent. The examples include real world applications involving directions and distances between locations. Key terms like included side are also defined. Practice problems are included for students to determine if a triangle congruence theorem can be used or additional information is needed.
The triangle inequality theorem states that the sum of any two side lengths of a triangle must be greater than the third side length. This means that if you are given two side lengths, you can determine the possible range of values for the third side length. The theorem can also be used to determine if three given side lengths could form a triangle. An example problem shows that sides of lengths 1, 2, and 3 do not form a triangle because 1 + 2 is not greater than 3.
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For a triangle to exist, the sum of the lengths of two sides must be greater than the length of the third side. The possible length of the third side of a triangle with sides of 6 and 12 must be greater than 6 and less than 18.
This document provides examples and explanations for proving triangle congruence using the Side-Side-Side (SSS) and Side-Angle-Side (SAS) postulates. It begins with definitions of key vocabulary like included angle. Example 1 uses SSS to prove two triangles congruent by showing that corresponding sides are congruent. Example 2 has students graph triangles on a coordinate plane and determine if they are congruent. Example 3 uses the midpoint theorem and vertical angles theorem to prove triangles congruent via SAS. The document concludes with practice problems for students.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This ensures that the three sides can form a triangle. Some key applications of the triangle inequality include determining if a set of lengths can form a triangle, solving triangle inequality equations, and relating side lengths to angle measures. For example, given a triangle with sides of 6 and 12 units, the third side must be greater than 6 units and less than 18 units to satisfy the triangle inequality.
The document discusses different methods for proving triangles are congruent: SSS, SAS, ASA, AAS, and HL. It states that if the specified corresponding parts of two triangles are congruent using one of these methods, then the triangles are congruent. The document provides examples of congruence proofs using these methods and their reasoning.
Triangle Inequality Theorem: Activities and Assessment MethodsMarianne McFadden
A comprehensive lesson on the Triangle Inequality Theorem, including pre-assessment, a hands-on activity (with rubric), and post-assessment methods that measure varying levels of achievement.
This learner modules talks about the Triangle Inequality. It also talks about the theorems & postulates that supports triangle inequalities in one or two triangles.
This document introduces special products and factors of polynomials. It discusses how patterns can be used to simplify algebraic expressions and solve geometric problems. Students will learn to identify special products through pattern recognition, find special products of polynomials, and apply these concepts to real-world problems. The goals are to demonstrate understanding of key concepts and solve practice problems accurately using different strategies.
This is a review game for a teacher to use in a geometry class. It goes over relationships in triangles, including bisetors, medians, altitudes, and inequalities and triangles.
Mathematics high school level quiz - Part IITfC-Edu-Team
The document outlines the format and questions for a mathematics quiz with multiple rounds. It begins with a two-part quiz where groups are given problem cards to solve. The subsequent rounds include warm-up questions testing concepts like geometry, averages, and number puzzles, as well as "real math" and logic rounds. Later rounds involve problem-solving, model-making to demonstrate algebraic identities, and a final written work discussion period.
The document outlines classroom rules and procedures for an activity called "Figure Me Out".
The classroom rules section establishes 7 rules for Queen Melvs' classroom: 1) Be on time, 2) Be active in class discussions, 3) Raise your hand to speak, 4) Respect others, 5) Avoid unnecessary noise, 6) Use appropriate language, and 7) Do your best.
The activity section describes a group word scramble game called "Figure Me Out". The mechanics are explained: 1) Students are divided into groups, 2) Groups study scrambled letters to form a word, 3) Arrange letters in 1 minute, 4) Raise board with answer, 5) Correct groups earn points, 6) Highest scoring
This document contains an overview of Chapter 10 from a geometry textbook. It covers the following topics across 10 lessons: solid figures, plane figures, problem-solving strategies like looking for patterns, lines/segments/rays, angles, and problem-solving investigations. The chapter introduces key concepts, provides examples, and aligns topics to state math standards. It aims to teach students to identify, describe, classify and solve problems involving various geometric shapes and their properties.
This document provides a summary of various maths concepts including:
- Square numbers are numbers multiplied by themselves such as 4 squared being 4 x 4 = 16.
- Multiples are numbers in times tables such as the multiples of 5 being 5, 10, 15, etc.
- Common large and small numbers include trillion, billion, million, thousand, and smaller denominations.
- Factors are numbers that divide evenly into another number like 1, 2, 3, 6 being factors of 12.
- Prime numbers can only be divided by 1 and themselves such as 5 and 97 being prime.
The document discusses methods for finding unknown values in data sets to achieve a predetermined measure of central tendency such as average, median, or mode. It explains the substitution and cover-up methods for determining a missing number needed to obtain a specific average. Examples walk through setting up and solving problems to find missing values using these methods.
The document appears to be a set of questions for a math quiz competition involving multiple rounds. It includes 10 questions per round, with topics ranging from prime numbers, sequences, shapes, operations, fractions, time, measurements, geometry, word problems, and more. Between each round, the participants are asked to swap papers to mark the answers from the previous round.
This document discusses solving linear equations in one unknown. It begins by listing 9 objectives related to understanding linear equations and using properties of equalities to solve them. Examples are then provided of solving linear equations by using addition, subtraction, multiplication, division and multiple properties. Techniques for expressing consecutive integers in terms of a variable are described. The document concludes by discussing George Polya's four steps for problem solving and providing example problems and solutions.
- The document provides information on teaching number facts for multiplication tables and angle measurement.
- It includes examples of using times tables to solve multiplication and division problems, as well as identifying different types of angles and calculating angles within shapes.
- Activities involve using protractors to measure angles, deriving angle measures for regular polygons, and exploring properties of interior and exterior angles in 2D shapes.
This is an initial attempt by my students of B.Ed. in creating Programmed Instructional material using the template I had provided them. Your observations and suggestions are welcome!
How to Pass IQ and Aptitude Tests: Practice Sample Questions and Answers with...How2become Ltd
Learn how to pass IQ and Aptitude Tests with ease with How2become. This presentation details the types of Aptitude tests you may come across and how to answer them. Full of expert tips and advice from the UK's leading careers specialist website. For 100s of free aptitude tests, try out our online psychometric tests here: http://www.mypsychometrictests.com/
This document contains 14 activities related to quadrilaterals and parallelograms. The activities involve identifying, classifying, constructing, and proving properties of different types of quadrilaterals. Students are asked to draw and measure quadrilaterals, find midpoints and diagonals, and justify properties of parallelograms, rectangles, rhombuses, kites, trapezoids, and other shapes. Questions provided with each activity assess students' understanding of key definitions and theorems about quadrilaterals.
A quadrilateral is a parallelogram if:
its opposite angles are equal, or.
its opposite sides are equal, or.
one pair of opposite sides are equal and parallel, or.
its diagonals bisect each other.
This document contains information about teaching GCSE mathematics, including an overview of topics, concepts, examples, homework, tests, and past papers. It also outlines the teaching methodology, which covers numbers, algebra, graphs, shape and space, sets, handling data, probability, and sequences and series. Finally, it provides details about several chapters in GCSE mathematics, including definitions of real numbers, properties of integers and rational numbers, and how to construct roots and use scientific notation.
A square has four equal sides and four right angles. A rectangle has four sides with opposite sides that are parallel and four right angles, though its sides are not necessarily equal in length like a square. The document provides information about squares and rectangles, including their properties, and presents a short quiz to test comprehension.
The document discusses mathematical reasoning and logic. It covers topics like statements and quantifiers, operations on sets like negation, compound statements using "and" and "or", implications and their antecedents and consequents, arguments using syllogisms and deduction. It also discusses the difference between deduction which reasons from general to specific, and induction which reasons from specific cases to a general conclusion.
The document discusses several key concepts regarding polynomials:
- Euclid's division algorithm states that any polynomial can be divided by a non-zero polynomial to obtain a quotient and remainder.
- The zeroes of a polynomial are the x-values where the graph crosses the x-axis.
- For a quadratic polynomial, the sum and product of its zeroes are related to its coefficients.
- Similar relationships exist between the zeroes and coefficients of cubic polynomials.
- Multiple choice and short answer questions are provided to test understanding of these concepts.
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving similar triangles. The module is designed to help students apply the definition of proportion to find unknown lengths, illustrate and verify the Basic Proportionality Theorem and its converse, and develop skills for solving geometry problems involving triangles. Exercises cover writing and simplifying ratios, setting up and solving proportions, determining if ratios form proportions, and applying the Basic Proportionality Theorem.
Weekly Dose 21 - Maths Olympiad PracticeKathleen Ong
- 5 kids A, B, C, D, E are sitting around a table with candies amounts of 10, 30, 20, 20, 40
- In each round, each kid gives half their candies to the kid on their right
- If a kid ends with an odd amount, they take 1 more from the table
- The question is if after several rounds all kids can have the same amount, and if so how much
I adopted a rescued kitten for a $21.94 fee and paid with a $20 bill and a $5 bill. After subtracting the $20 bill from the fee, I owed $1.94. Subtracting the $1.94 from the $5 bill, my change was $3.06.
Calvin J. Williams graduated from Northwest High School in 2003 where he studied auto mechanics and received high grades in math, science, and auto mechanics. He has work experience at Steiner's Service Station and AA Appliance Repair Shop and his goal is to become a licensed auto mechanic and own his own auto repair shop.
What is Accounting & the Accounting Equationjpalmertree
The document provides a quiz on accounting concepts with multiple choice questions in various categories like accounting concepts, critical thinking, key terms, and solving equations. It tests understanding of basic accounting principles like the accounting equation, distinguishing between assets, liabilities and owner's equity, and how transactions affect financial statements. The quiz is designed to help students learn and be assessed on foundational accounting knowledge.
The document provides instructions for playing a game to align stars by having teams answer questions correctly. Teams are assigned a color and the first team to get 3, 4, or 5 stars in a row touching by color wins. The stars can be aligned in rows, columns or diagonally on the game board.
Review of Supply & Demand and the Marketjpalmertree
This document contains a series of graphs and questions related to reading and interpreting graphs about supply and demand concepts. There are 9 questions total across different topics like reading supply/demand curves, price controls, equilibrium price, quantity supplied/demanded, elasticity, and key economic terms. The questions require analyzing the graphs to determine values like price, quantity, or type of good/market based on changes in supply and demand.
This document discusses key events and people related to several major themes in late 19th and early 20th century American history, including the Spanish-American War, Theodore Roosevelt's presidency, civil rights and women's suffrage movements, progressivism, socialism, populism, and imperialism. It provides questions to test understanding with short answers about treaties ending wars, amendments, court cases, and more.
The document provides instructions for playing a game called "Align the Stars" which involves dividing players into teams, choosing a color for each team, and answering trivia questions to earn stars of their team's color in order to be the first to get a set number of stars in a row, column, or diagonal to win. It also provides a sample game board layout and questions to be asked.
The document is a quiz about types of government, the US Constitution and Bill of Rights. It contains multiple choice questions about concepts such as democracy, dictatorship, monarchy, amendments, separation of powers, and more. Players from two teams earned points for answering questions correctly within time limits.
The document provides step-by-step instructions for solving different types of inequalities involving multiplication, division, addition, and subtraction. It explains that to isolate the variable, the same steps are followed as with equations but the sign of the inequality must be preserved. Examples shown include subtracting, dividing, and multiplying both sides of the inequality as needed to isolate the variable.
The document provides instructions for solving different types of inequalities through addition, subtraction, and isolating variables. It explains that to solve inequalities, you treat them similarly to equations by applying the same operations to both sides so as not to change the relationship. The examples walk through solving linear inequalities with whole numbers and fractions by adding or subtracting values from both sides to isolate the variable. It also discusses combining like terms when they appear in an inequality.
To view this slideshow properly, you will need to click on the "download" link, download the PowerPoint file, and then open it up in Microsoft PowerPoint and view the slideshow.
The document discusses various grammar concepts including ambiguous pronouns, misplaced modifiers, figurative language, subject-verb agreement, and text structures. It provides examples of sentences containing errors in these areas and asks the reader to identify and correct the errors. It also asks the reader to identify examples of figurative language and text structures.
This is a PowerPoint presentation to be used when studying vocabulary words for Of Mice and Men. The words are pronounced and defined, and interesting animations and sound effects are included.
This document contains definitions for 8 vocabulary words: avaricious means greedy for riches, credulity means tendency to believe too readily, doughty means brave or valiant, furtively means secretly or stealthily, fusillade refers to something like the rapid firing of many firearms, maligned means spoken ill of, and prosaic means commonplace or ordinary.
1. The document provides directions for a scavenger hunt activity involving questions about topics from early 20th century American history, such as technology, mass production, immigration, labor, and politics.
2. The questions cover inventions like the internal combustion engine, the rise of mass production and assembly lines, immigration patterns and the resulting social attitudes, labor issues faced by immigrants and the growth of unions, and political machines in cities.
3. Upon completing the various history-related questions in the scavenger hunt, students were instructed to email their instructor to receive points for the completed activity.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
3. Bisectors, Medians, & Altitudes: 2 Points
In ∆GHJ, HP=5x-16, H
N
PJ=3x+8, m<GJN=6y-3,
m<NJH=4y+23, &
m<HMG=4z+14 G P
Stop!
M
Time’s Up!
The Question Is :
J
GP is a median of ∆GHJ. Find HJ.
The Answer Is :
88
4. Bisectors, Medians, & Altitudes: 3 Points
In ∆GHJ, HP=5x-16, H
N
PJ=3x+8, m<GJN=6y-3,
m<NJH=4y+23, &
m<HMG=4z+14 G P
Stop!
The Question Is : M
Time’s bisector.
Find m<GJN if JN is an angle
Up! J
The Answer Is :
150
5. Bisectors, Medians, & Altitudes: 4 Points
In ∆GHJ, HP=5x-16, H
N
PJ=3x+8, m<GJN=6y-3,
m<NJH=4y+23, &
m<HMG=4z+14 G P
Stop!
M
The Question Is :
Time’s find the value of
If HM is an altitude of ∆GHJ,
Up! J
z.
The Answer Is :
19
6. Bisectors, Medians, & Altitudes: 5 Points
The Question Is :
All of the angle bisectors of a triangle meet at
the _________. Stop!
Time’s Up!
The Answer Is :
incenter
7. Bisectors, Medians, & Altitudes: 6 Points
CP is an altitude, CQ is the C
angle bisector of <ACB, and R is
the midpoint of AB.
The Question Is : Stop!
and m<QCB=42+x.
Time’s Up! P
Find m<ACQ if m<ACB=123-x
A Q R B
The Answer Is :
m<ACQ = 55
8. Bisectors, Medians, & Altitudes: 7 Points
CP is an altitude, CQ is the C
angle bisector of <ACB, and R is
the midpoint of AB.
The Question Is : Stop!
Find AB if AR=3x+6 and
RB=5x-14 Time’s Up! P
A Q R B
The Answer Is :
AB = 72
9. Bisectors, Medians, & Altitudes: 8 Points
The Question Is :
In ∆RST, if the point P is the midpoint of RS,
Stop!
then PT is a(n) ________.
The AnswerTime’s Up!
Is :
median
10. Bisectors, Medians, & Altitudes: 9 Points
The Question Is :
What are the special segments of triangles?
Stop!
Time’s Up!
The Answer Is :
Perpendicular bisectors, medians, angle
bisectors, and altitudes
11. Indirect Proof: 2 Points
The Question Is :
When using _________, you assume that the
conclusion false and then show that this assumption
Stop!
leads to a contradiction of the hypothesis, or some
other accepted fact, such a definition, postulate,
Time’s Up!
theorem, or corollary.
The Answer Is :
Indirect reasoning
12. Indirect Proof: 3 Points
The Question Is :
True or False: Another name for an indirect
proof is a proof by contradiction.
Stop!
Time’s Up!
The Answer Is :
True
13. Indirect Proof: 4 Points
The Question Is :
What are the three steps of writing an indirect proof.
The Answer Is :
1. Assume that the conclusion is false
Stop!
2. Show that this assumption leads to a
Time’s Up!
contradiction of the hypothesis, or some other
fact, such as a definition, postulate, theorem, or
corollary
3. Point out that because the false conclusion leads
to an incorrect statement, the
original conclusion must be true
14. Indirect Proof: 5 Points
The Question Is :
State the assumption you would make to
start an indirect proof of the following
Stop!
statement: EF is not a perpendicular bisector.
Time’s Up!
The Answer Is :
EF is a perpendicular bisector.
15. Indirect Proof: 6 Points
The Question Is :
State the assumption you would make to
start an indirect proof of the following
Stop!
statement: If 5x < 25, then x < 5.
Time’s Up!
The Answer Is :
x>5
16. Indirect Proof: 7 Points
The Question Is :
State the assumption you would make to start an
indirect proof of the following statement: If a
rational number is any number that can be
Stop!
expressed as a/b, where a and b are integers and b
is not equal to 0, 6 is a rational number.
Time’s Up!
The Answer Is :
6 cannot be expressed as a/b, where
a & b are integers and b is not equal
to 0.
17. Indirect Proof: 7 Points
The Question Is :
State the assumption you would make to start an
indirect proof of the following statement: The angle
bisector of the vertex angle of an isosceles triangle
Stop!
is also an altitude of the triangle.
Time’s Up!
The Answer Is :
The angle bisector of the vertex angle of an isosceles
triangle is not an altitude of the triangle.
18. Indirect Proof: 9 Points
The Question Is :
State the assumption you would make to start an
indirect proof of the following statement: Two lines
Stop!
that are cut by a transversal so that alternate
interior angles are congruent are parallel.
The Answer Is :
Time’s Up!
The lines are not parallel
19. Inequalities & Triangles: 2 Points
The Question Is :
What is the definition of an inequality?
The Answer Is :
Stop!
For any real numbers a and b,Up!if and only if
Time’s a > b
there is a positive number c such that a = b + c.
20. Inequalities & Triangles: 3 Points
The Question Is :
What are the four properties of Inequalities for
Real Numbers?
Stop!
The Answer Is :
Time’s Up!
Comparison Property, Transitive Property,
Addition and Subtraction Properties, &
Multiplication and Division Properties
21. Inequalities & Triangles: 4 Points
The Question Is :
What does the “Comparison Property” say?
Stop!
The Answer Is :
Time’s Up!
a < b, a = b, or a > b
22. Inequalities & Triangles: 5 Points
The Question Is : 7
4
Use the Exterior Angle
Inequality Theorem to list
Stop!
all angles that satisfy the
stated condition: measures
less than m<1 Time’s Up! 5
6
8
3
2
1
The Answer Is :
<4, <5, <6
23. Inequalities & Triangles: 6 Points
The Question Is : 7
4
Determine the angle with the
Greatest measure: <1, <2, <3.
Stop!
The Answer Is : Time’s Up! 5
8
2
1
6 3
<1
24. Inequalities & Triangles: 7 Points
The Question Is :
Determine the angle with the
8
Greatest measure: <8, <5, <7. 7
Stop! 5
The Answer Is : Time’s Up!
<5
25. Inequalities & Triangles: 8 Points
The Question Is :
6
Determine the angle with the
8
Greatest measure: <6, <7, <8. 7
Stop!
The Answer Is :Time’s Up!
<8
26. Inequalities & Triangles: 9 Points
The Question Is :
Determine the angle with the 6
Greatest measure: <1, <6, <9. 1
Stop! 9
The Answer Is : Time’s Up!
<1
27. The Triangle Inequality : 2 Points
The Question Is :
What is the “Triangle Inequality Theorem?”
The Answer Is :
Stop!
The sum of the lengths of anyUp!
Time’s two sides of a triangle is
greater than the length of the third side.
28. The Triangle Inequality : 3 Points
The Question Is :
What is the “Triangle Inequality Theorem” used to
determine?
Stop!
The Answer Is :
Time’s Up!
Whether three segments can form a triangle.
29. The Triangle Inequality : 4 Points
The Question Is :
If a line is horizontal, the shortest distance from a point
to that line will be along a _______ line. Likewise, the
Stop!
shortest distance from a point to a vertical line lies
along a ________ line.
Time’s Up!
The Answer Is :
vertical, horizontal
30. The Triangle Inequality : 5 Points
The Question Is :
The ________ segment from a point to a line is the
shortest segment from the point to the line.
Stop!
Time’s Up!
The Answer Is :
perpendicular
31. The Triangle Inequality : 6 Points
The Question Is :
Can the following lengths be the lengths of the sides of
a triangle: 1, 2, 3? Explain.
Stop!
The Answer Is :
Time’s Up!
No; 1 + 2 is not greater than 3
32. The Triangle Inequality : 7 Points
The Question Is :
Find the range for the measure of the third side: 5 and
11.
Stop!
The Answer Is :Time’s Up!
6 < n <16
33. The Triangle Inequality : 8 Points
The Question Is :
Determine whether or not the given measures can be
Stop!
the lengths of the sides of a triangle: 9, 21, 20. Explain.
Time’s Up!
The Answer Is :
Yes; 9 + 20 > 21
34. The Triangle Inequality : 9 Points
The Question Is :
Find the range for the measure of the third side of the
triangle: 21 and 47.
Stop!
The Answer Is :Time’s Up!
26 < n < 68
35. Inequalities Involving 2 Triangles: 2 Points
The Question Is :
What does the “SAS Inequality” state?
The Answer Is : Stop!
Two sides of a triangle are congruent to two sides of
another triangle. Time’s Up! in the first
If the included angle
triangle has a greater measure than the included angle
in the second triangle, then the 3rd side
Of the first triangle is longer than the
3rd side of the second.
36. Inequalities Involving 2 Triangles: 3 Points
The Question Is :
What is another name for the “SAS Inequality
Theorem?”
Stop!
The Answer Is :
Time’s Up!
The “Hinge Theorem.”
37. Inequalities Involving 2 Triangles: 4 Points
The Question Is :
What does the “SSS Inequality Theorem” state?
The Answer Is :
Stop! to 2 sides of
If 2 sides of a triangle are congruent
Time’s other, then the angle
rd
Up!
another triangle, and the 3 side in one triangle is
rd
longer than the 3 side in the
between the pair of congruent sides in the 1st triangle
is greater than the corresponding angle in the 2nd
triangle.
38. Inequalities Involving 2 Triangles: 5 Points
15 A
The Question Is : D 20
Write an inequality
relating AB and CD. 50 B
Stop!
The Answer Is : 15
AB < CD
Time’s Up!
C
39. Inequalities Involving 2 Triangles: 6 Points
The Question Is : x+5
Write an inequality 45
relating AB and CD. 3x - 7
Stop!
The Answer Is :
Time’s Up!
7/3 < x <6
40. Inequalities Involving 2 Triangles: 7 Points
The Question Is : 4 C
B
Write an inequality relating 6
the given pair of angles
Stop!
or segments: AB, FD. 9 6
9
D
The Answer Is :
Time’s Up!
A
F
6
10
AB > FD
41. Inequalities Involving 2 Triangles: 8 Points
The Question Is : 4 C
B
Write an inequality relating 6
the given pair of angles
9
or segments: m<BDC,
m<FDB.
Stop!
9 6
D
Time’s Up!
A
10 F
6
The Answer Is :
M<BDC < m<FDB
42. Inequalities Involving 2 Triangles: 9 Points
The Question Is : 4 C
B
Write an inequality relating 6
the given pair of angles
m<DBF.
Stop!
or segments: m<FBA, 9 6
9
D
The Answer Is :
Time’s Up!
A
10 F
6
m<FBA > m<DBF