Congruence of triangle
•Download as PPTX, PDF•
4 likes•7,815 views
The document discusses different types of triangles and rules for determining if triangles are congruent. It defines congruent figures as those that are equal in size and shape and can cover each other completely. It then provides four rules for triangle congruence: SAS, ASA, SSS, and RHS. These rules state that triangles are congruent if their corresponding sides and/or angles are equal.
Report
Share
Report
Share
Recommended
Triangle Class-9th
This document discusses triangles and congruence. It defines a triangle as a closed figure with three intersecting lines and as having three sides, three angles, and three vertices. It then explains the meaning of congruence as equal in all respects and introduces three rules for determining if triangles are congruent: the Side-Angle-Side rule, the Angle-Side-Angle rule, and the Angle-Angle-Side rule. The document concludes with assigning homework questions involving congruent triangles.
Triangle
The document discusses triangles and their properties. It defines a triangle as a closed figure formed by three intersecting lines with three sides, three angles, and three vertices. Two triangles are congruent if corresponding sides and angles are equal. There are five rules for triangle congruence based on sides and angles: SAS, ASA, AAS, SSS, and RHS. Inequalities in a triangle relate side lengths to opposite angles - the longer the side, the larger the opposite angle, and the third side is always smaller than the sum of the other two sides. The document was prepared by Vyom Bhardwaj, a student in 9th B with roll number 37.
Triangles
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
PPT ON TRIANGLES FOR CLASS X
1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.
Basics of Quadrilaterals
This document defines and describes different types of quadrilaterals. A quadrilateral is a shape with four sides. There are several specific types of quadrilaterals including rectangles, squares, rhombi, parallelograms, trapezoids, and kites. Each type has distinct properties, such as pairs of parallel or equal sides. The document also proves that the sum of the interior angles of any quadrilateral is always 360 degrees.
Triangles and its properties
The document defines and describes different types of triangles based on their sides and angles. It discusses scalene, isosceles, equilateral, acute-angled, right-angled, and obtuse-angled triangles. It also outlines some key properties of triangles, including that they have three sides and three angles, medians connect vertices to midpoints of opposite sides, altitudes are perpendicular from vertices to opposite sides, exterior angles equal the sum of interior opposite angles, and isosceles triangles have equal angles opposite equal sides. The Pythagorean theorem is also summarized.
ppt on Triangles Class 9
1. The document defines triangles and their properties including three sides, three angles, and three vertices.
2. It explains five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Some properties of triangles discussed are: angles opposite equal sides are equal, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.
R.TANUJ Maths Triangles for Class IX
1. The document discusses different types of triangles based on their sides and angles. It defines triangle congruence and presents several triangle congruence theorems including SAS, ASA, AAS, SSS, and RHS.
2. Properties of triangles such as corresponding angles and sides of congruent triangles being equal are explained. Inequalities in triangles and relationships between sides and angles are also covered.
3. Objectives of the lesson include defining triangle congruence, stating criteria for congruence, and properties of triangles like sum of angles and relationships between sides and angles.
Recommended
Triangle Class-9th
This document discusses triangles and congruence. It defines a triangle as a closed figure with three intersecting lines and as having three sides, three angles, and three vertices. It then explains the meaning of congruence as equal in all respects and introduces three rules for determining if triangles are congruent: the Side-Angle-Side rule, the Angle-Side-Angle rule, and the Angle-Angle-Side rule. The document concludes with assigning homework questions involving congruent triangles.
Triangle
The document discusses triangles and their properties. It defines a triangle as a closed figure formed by three intersecting lines with three sides, three angles, and three vertices. Two triangles are congruent if corresponding sides and angles are equal. There are five rules for triangle congruence based on sides and angles: SAS, ASA, AAS, SSS, and RHS. Inequalities in a triangle relate side lengths to opposite angles - the longer the side, the larger the opposite angle, and the third side is always smaller than the sum of the other two sides. The document was prepared by Vyom Bhardwaj, a student in 9th B with roll number 37.
Triangles
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
PPT ON TRIANGLES FOR CLASS X
1. The document discusses properties and congruence of triangles. It defines congruence as two triangles being the same shape and size with corresponding angles and sides equal.
2. There are five criteria for congruence: side-angle-side, angle-side-angle, angle-angle-side, side-side-side, and right angle-hypotenuse-side.
3. Additional properties discussed include isosceles triangles having equal angles opposite equal sides, and relationships between sides and opposite angles/angles and opposite sides in all triangles.
Basics of Quadrilaterals
This document defines and describes different types of quadrilaterals. A quadrilateral is a shape with four sides. There are several specific types of quadrilaterals including rectangles, squares, rhombi, parallelograms, trapezoids, and kites. Each type has distinct properties, such as pairs of parallel or equal sides. The document also proves that the sum of the interior angles of any quadrilateral is always 360 degrees.
Triangles and its properties
The document defines and describes different types of triangles based on their sides and angles. It discusses scalene, isosceles, equilateral, acute-angled, right-angled, and obtuse-angled triangles. It also outlines some key properties of triangles, including that they have three sides and three angles, medians connect vertices to midpoints of opposite sides, altitudes are perpendicular from vertices to opposite sides, exterior angles equal the sum of interior opposite angles, and isosceles triangles have equal angles opposite equal sides. The Pythagorean theorem is also summarized.
ppt on Triangles Class 9
1. The document defines triangles and their properties including three sides, three angles, and three vertices.
2. It explains five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Some properties of triangles discussed are: angles opposite equal sides are equal, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.
R.TANUJ Maths Triangles for Class IX
1. The document discusses different types of triangles based on their sides and angles. It defines triangle congruence and presents several triangle congruence theorems including SAS, ASA, AAS, SSS, and RHS.
2. Properties of triangles such as corresponding angles and sides of congruent triangles being equal are explained. Inequalities in triangles and relationships between sides and angles are also covered.
3. Objectives of the lesson include defining triangle congruence, stating criteria for congruence, and properties of triangles like sum of angles and relationships between sides and angles.
Types of triangles
It gives information regarding triangles, their types & properties in mathematics. Helpful to school students.
Triangles (Similarity)
The document is an acknowledgement from a group of 5 students - Abhishek Mahto, Lakshya Kumar, Mohan Kumar, Ritik Kumar, and Vivek Singh of class X E. They are thanking their principal Dr. S.V. Sharma and math teacher Mrs. Shweta Bhati for their guidance and support in completing their project on triangles and similarity. They also thank their parents and group members for their advice and assistance during the project.
Mathematics project
Triangles can be classified based on the number of congruent sides. There are three types of triangles: scalene (no congruent sides), isosceles (at least two congruent sides), and equilateral (three congruent sides). Heron's formula provides a way to calculate the area of any triangle using the lengths of its three sides. The formula is: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (sum of sides divided by 2). The document also presents a researched formula for calculating the area of an equilateral triangle using only the length of one side.
Triangles
Triangles are three-sided polygons that have three angles and three sides. There are three main types of triangles based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). The interior angles of any triangle always sum to 180 degrees. Important triangle properties include the exterior angle theorem, Pythagorean theorem, and congruency criteria like SSS, SAS, ASA. Common secondary parts are the median, altitude, angle bisector, and perpendicular bisector. The area of triangles can be found using Heron's formula or other formulas based on side lengths and types of triangles.
Triangles X CLASS CBSE NCERT
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of similar triangles, including the AAA, SSS, SAS, and AA similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles discussed include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Mensuration PPT CLASS 8 NCERT
INCLUDES ALL THE FORMULAS FOR SOLVING SUMS,DEPENDING UPON NCERT PUBLICATION FOR CLASS 8
MAKES STUDYING EASIER,USEFUL FOR MAKING PPT CAN USE TO MAKE PPT
Triangles and their properties
This document discusses properties of triangles, including classifications based on sides (equilateral, isosceles, scalene) and angles (acute). It outlines key properties such as: the sum of interior angles is 180 degrees; the exterior angle is equal to the sum of the two non-adjacent interior angles; and the triangle inequality stating the sum of any two sides must be greater than the third side. Congruence of triangles is also discussed, noting triangles are congruent when corresponding sides and angles are equal, and can be proven using ASA, SAS, or SSS criteria.
Understanding Quadrilaterals
This won 2nd at cluster level and 1st at Regional level but unfortunately PPT Event was not scheduled for Nationals.
Quadrilaterals
This document presents a summary of quadrilaterals for a class of 9th grade students. It defines a quadrilateral as a four-sided polygon and discusses the key components such as vertices, sides, angles, and diagonals. It then explains different types of quadrilaterals like parallelograms, rectangles, squares, rhombi, trapezoids, and kites. The properties of parallelograms, rectangles, rhombi, and squares are outlined. The document concludes by listing the student team members who created the presentation.
Properties of Quadrilaterals
This document defines and provides properties of various quadrilaterals: squares have equal sides and right angles; parallelograms have opposite sides that are equal and parallel; kites have perpendicular diagonals with the longer diagonal bisecting the shorter; trapezoids have one set of parallel sides; rectangles have opposite sides that are equal length and parallel with right angles; and rhombuses have equal sides and diagonals that bisect and are perpendicular to each other. Cool facts about squares include that they are also parallelograms, rhombuses, trapezoids, and rectangles with 4 lines of symmetry and specific relationships between sides, angles, and diagonals. Formulas for perimeter and area of some shapes
Triangles and its all types
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Triangles and it's properties
this is a power point presentation related to the topic triangle and it's properties on the subject math
'like and support'
Triangle
An acute triangle has all angles less than 90 degrees. An obtuse triangle has one angle greater than 90 degrees. A right triangle has one 90 degree angle. Triangles can also be classified based on their side lengths as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides unequal). The perimeter of a triangle is calculated by adding the lengths of all three sides. The area of a triangle is calculated using the formula Area = (base x height) / 2, where the base is the length of one side and the height is the length of the line drawn perpendicular to the base from the opposite vertex.
Congruence of triangles
This document discusses congruence of triangles, which is when two triangles have the same shape and size, meaning one triangle can be repositioned to coincide precisely with the other. It provides examples of congruent and non-congruent triangles based on equal angles and side lengths. The key properties for congruence of triangles are that they must have equal measures of angles and equal lengths of sides.
Data handling class 8th
This video from SK Knowledge Point discusses different types of diagrams used to represent numerical data, including pictographs, bar graphs, double bar graphs, pie charts, and histograms. It explains that pictographs use symbols to represent data values, while bar graphs and histograms use bars to show frequencies. Pie charts represent parts of a whole through proportional sectors of a circle. Various examples are provided of each type of diagram. The video encourages viewers to like, share and subscribe to the channel for more math content.
Mathsproject quadrilaterals
1) A quadrilateral is a polygon with four sides and four vertices. There are over 9 million types of quadrilaterals that can be classified as simple or complex.
2) Quadrilaterals include parallelograms, trapezoids, kites, and more. A parallelogram has two sets of parallel sides and opposite/adjacent angles are equal. A square is a special type of rectangle and parallelogram.
3) The interior angles of any quadrilateral sum to 360 degrees. The line segment between the midpoints of two sides of a triangle is parallel to the third side and half its length.
Math's ppt on triangles
Triangles can be classified based on side lengths as equilateral, isosceles, or scalene triangles and based on angles as acute, obtuse, or right triangles. The three main properties of triangles are the angle sum property, exterior angle property, and Pythagorean theorem. Secondary parts of a triangle include the median, altitude, perpendicular bisector, and angle bisector. Triangles can be proven congruent using the SSS, SAS, ASA, AAS, or RHS criteria. Inequalities in triangles relate longer sides to larger angles and shorter sides to smaller angles. Important centers of a triangle include the incenter, circumcenter, centroid, and orthocenter.
Triangle and its properties
This presentation discusses properties of triangles, including:
- Classifying triangles by side lengths as scalene, isosceles, or equilateral.
- Classifying triangles by angle measures as acute, obtuse, or right.
- Defining medians and altitudes of triangles.
- Proving properties such as the angle sum theorem, the exterior angle theorem, and Pythagorean theorem.
Congruence Of Triangle
This document discusses congruence of triangles in mathematics. It defines congruence as two shapes being equal in shape, size, and area or coinciding exactly when placed on top of each other. There are five criteria for triangle congruence: side-side-side (SSS), side-angle-side (SAS), angle-angle-side (AAS), angle-side-angle (ASA), and right-angle-hypotenuse-side (RHS). Each rule states that if the given sides or angles are equal, then the triangles are congruent. Examples are provided to illustrate each rule.
Triangles -Classroom presentation
Elements of a Triangle
Types of Triangles
Properties of Triangles
Angle sum property of a Triangle
Side property of a Triangle
Congruence of Triangle
The document discusses different rules for determining if two triangles are congruent, including:
- The ASA (Angle-Side-Angle) rule, which states two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle. An example proof of this rule is provided.
- The SSS (Side-Side-Side) rule, which states two triangles are congruent if three sides of one triangle are equal to the corresponding three sides of the other triangle. An example proof is also provided.
- The Hypotenuse-Leg rule, which states two right triangles are congruent if the hypotenuse and one side of one
Congruent triangles theorem
This document discusses triangle congruence theorems. It defines the five main congruence theorems: ASA, SAS, SSS, AAS, and introduces four additional theorems for right triangles only: HL, HA, LL, LA. Examples are provided to demonstrate applying each theorem to determine if two triangles are congruent based on given side or angle information.
More Related Content
What's hot
Types of triangles
It gives information regarding triangles, their types & properties in mathematics. Helpful to school students.
Triangles (Similarity)
The document is an acknowledgement from a group of 5 students - Abhishek Mahto, Lakshya Kumar, Mohan Kumar, Ritik Kumar, and Vivek Singh of class X E. They are thanking their principal Dr. S.V. Sharma and math teacher Mrs. Shweta Bhati for their guidance and support in completing their project on triangles and similarity. They also thank their parents and group members for their advice and assistance during the project.
Mathematics project
Triangles can be classified based on the number of congruent sides. There are three types of triangles: scalene (no congruent sides), isosceles (at least two congruent sides), and equilateral (three congruent sides). Heron's formula provides a way to calculate the area of any triangle using the lengths of its three sides. The formula is: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (sum of sides divided by 2). The document also presents a researched formula for calculating the area of an equilateral triangle using only the length of one side.
Triangles
Triangles are three-sided polygons that have three angles and three sides. There are three main types of triangles based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). The interior angles of any triangle always sum to 180 degrees. Important triangle properties include the exterior angle theorem, Pythagorean theorem, and congruency criteria like SSS, SAS, ASA. Common secondary parts are the median, altitude, angle bisector, and perpendicular bisector. The area of triangles can be found using Heron's formula or other formulas based on side lengths and types of triangles.
Triangles X CLASS CBSE NCERT
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of similar triangles, including the AAA, SSS, SAS, and AA similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles discussed include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Mensuration PPT CLASS 8 NCERT
INCLUDES ALL THE FORMULAS FOR SOLVING SUMS,DEPENDING UPON NCERT PUBLICATION FOR CLASS 8
MAKES STUDYING EASIER,USEFUL FOR MAKING PPT CAN USE TO MAKE PPT
Triangles and their properties
This document discusses properties of triangles, including classifications based on sides (equilateral, isosceles, scalene) and angles (acute). It outlines key properties such as: the sum of interior angles is 180 degrees; the exterior angle is equal to the sum of the two non-adjacent interior angles; and the triangle inequality stating the sum of any two sides must be greater than the third side. Congruence of triangles is also discussed, noting triangles are congruent when corresponding sides and angles are equal, and can be proven using ASA, SAS, or SSS criteria.
Understanding Quadrilaterals
This won 2nd at cluster level and 1st at Regional level but unfortunately PPT Event was not scheduled for Nationals.
Quadrilaterals
This document presents a summary of quadrilaterals for a class of 9th grade students. It defines a quadrilateral as a four-sided polygon and discusses the key components such as vertices, sides, angles, and diagonals. It then explains different types of quadrilaterals like parallelograms, rectangles, squares, rhombi, trapezoids, and kites. The properties of parallelograms, rectangles, rhombi, and squares are outlined. The document concludes by listing the student team members who created the presentation.
Properties of Quadrilaterals
This document defines and provides properties of various quadrilaterals: squares have equal sides and right angles; parallelograms have opposite sides that are equal and parallel; kites have perpendicular diagonals with the longer diagonal bisecting the shorter; trapezoids have one set of parallel sides; rectangles have opposite sides that are equal length and parallel with right angles; and rhombuses have equal sides and diagonals that bisect and are perpendicular to each other. Cool facts about squares include that they are also parallelograms, rhombuses, trapezoids, and rectangles with 4 lines of symmetry and specific relationships between sides, angles, and diagonals. Formulas for perimeter and area of some shapes
Triangles and its all types
This document defines and describes different types of triangles based on side lengths and angle measures. It also discusses properties of triangles related to similarity, including the AAA, SSS, SAS, and RHS similarity criteria. Properties of special right triangles and the Pythagorean theorem are also covered. Types of triangles described include scalene, isosceles, equilateral, acute, obtuse, and right triangles.
Triangles and it's properties
this is a power point presentation related to the topic triangle and it's properties on the subject math
'like and support'
Triangle
An acute triangle has all angles less than 90 degrees. An obtuse triangle has one angle greater than 90 degrees. A right triangle has one 90 degree angle. Triangles can also be classified based on their side lengths as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides unequal). The perimeter of a triangle is calculated by adding the lengths of all three sides. The area of a triangle is calculated using the formula Area = (base x height) / 2, where the base is the length of one side and the height is the length of the line drawn perpendicular to the base from the opposite vertex.
Congruence of triangles
This document discusses congruence of triangles, which is when two triangles have the same shape and size, meaning one triangle can be repositioned to coincide precisely with the other. It provides examples of congruent and non-congruent triangles based on equal angles and side lengths. The key properties for congruence of triangles are that they must have equal measures of angles and equal lengths of sides.
Data handling class 8th
This video from SK Knowledge Point discusses different types of diagrams used to represent numerical data, including pictographs, bar graphs, double bar graphs, pie charts, and histograms. It explains that pictographs use symbols to represent data values, while bar graphs and histograms use bars to show frequencies. Pie charts represent parts of a whole through proportional sectors of a circle. Various examples are provided of each type of diagram. The video encourages viewers to like, share and subscribe to the channel for more math content.
Mathsproject quadrilaterals
1) A quadrilateral is a polygon with four sides and four vertices. There are over 9 million types of quadrilaterals that can be classified as simple or complex.
2) Quadrilaterals include parallelograms, trapezoids, kites, and more. A parallelogram has two sets of parallel sides and opposite/adjacent angles are equal. A square is a special type of rectangle and parallelogram.
3) The interior angles of any quadrilateral sum to 360 degrees. The line segment between the midpoints of two sides of a triangle is parallel to the third side and half its length.
Math's ppt on triangles
Triangles can be classified based on side lengths as equilateral, isosceles, or scalene triangles and based on angles as acute, obtuse, or right triangles. The three main properties of triangles are the angle sum property, exterior angle property, and Pythagorean theorem. Secondary parts of a triangle include the median, altitude, perpendicular bisector, and angle bisector. Triangles can be proven congruent using the SSS, SAS, ASA, AAS, or RHS criteria. Inequalities in triangles relate longer sides to larger angles and shorter sides to smaller angles. Important centers of a triangle include the incenter, circumcenter, centroid, and orthocenter.
Triangle and its properties
This presentation discusses properties of triangles, including:
- Classifying triangles by side lengths as scalene, isosceles, or equilateral.
- Classifying triangles by angle measures as acute, obtuse, or right.
- Defining medians and altitudes of triangles.
- Proving properties such as the angle sum theorem, the exterior angle theorem, and Pythagorean theorem.
Congruence Of Triangle
This document discusses congruence of triangles in mathematics. It defines congruence as two shapes being equal in shape, size, and area or coinciding exactly when placed on top of each other. There are five criteria for triangle congruence: side-side-side (SSS), side-angle-side (SAS), angle-angle-side (AAS), angle-side-angle (ASA), and right-angle-hypotenuse-side (RHS). Each rule states that if the given sides or angles are equal, then the triangles are congruent. Examples are provided to illustrate each rule.
Triangles -Classroom presentation
Elements of a Triangle
Types of Triangles
Properties of Triangles
Angle sum property of a Triangle
Side property of a Triangle
What's hot (20)
Viewers also liked
Congruence of Triangle
The document discusses different rules for determining if two triangles are congruent, including:
- The ASA (Angle-Side-Angle) rule, which states two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle. An example proof of this rule is provided.
- The SSS (Side-Side-Side) rule, which states two triangles are congruent if three sides of one triangle are equal to the corresponding three sides of the other triangle. An example proof is also provided.
- The Hypotenuse-Leg rule, which states two right triangles are congruent if the hypotenuse and one side of one
Congruent triangles theorem
This document discusses triangle congruence theorems. It defines the five main congruence theorems: ASA, SAS, SSS, AAS, and introduces four additional theorems for right triangles only: HL, HA, LL, LA. Examples are provided to demonstrate applying each theorem to determine if two triangles are congruent based on given side or angle information.
First Year Teacher Training (afternoon session)- Content
This document provides an overview and resources for new teachers attending a first year teacher training. It includes:
- A reminder that the training is an opportunity to ask questions, share resources, and keep the conversation going online.
- Links to key websites that outline the Common Core and Essential Standards that teachers need to teach, including standard division documents, unpacking documents and graphic organizers.
- Suggestions to explore the standards documents in detail to understand what exactly needs to be taught and guidance on when to teach certain concepts.
- An overview of the assessments that will be used in elementary, middle, and high school along with contacts for instructional support in different subject areas.
Rational numbers
This document discusses operations with rational numbers such as addition, subtraction, multiplication, and division. It explains that for addition and subtraction of rational numbers with common denominators, only the numerators are added or subtracted. For different denominators, the lowest common denominator must first be found before adding or subtracting the numerators. Multiplication of rational numbers is done by multiplying the numerators and denominators. Division can be performed by multiplying the first number by the reciprocal of the second number.
Maths rational numbers
Whole numbers are closed under addition and multiplication, meaning any sum or product of whole numbers is also a whole number. However, whole numbers are not closed under subtraction or division, as subtracting or dividing whole numbers can produce numbers with fractions or decimals.
Basic geometrical ideas class vi
Geometry is the branch of mathematics that deals with figures like points, lines, angles, surfaces, and solids. It studies their properties and relationships. A point has no size, a line extends indefinitely, a ray has one endpoint and extends from it, a plane is a flat surface that goes on forever, an angle is formed by two rays from the same point, a triangle has three sides and three angles, a quadrilateral is a four-sided figure, and a circle is all points the same distance from the center. The document teaches the basic geometric concepts to students.
comparing quantities class 8
This document contains information about ratios, percentages, discounts, simple and compound interest, and amounts. It includes definitions and formulas for these topics, as well as examples of calculations for ratio, percentage increase/decrease, discount percentage, sales tax, and simple and compound interest. The document concludes with a short summary of key points about discounts, cost price, sales tax, and the formulas for calculating compound interest annually and half-yearly.
Rational numbers
Rational numbers can be defined as any number that can be made by dividing one integer by another. This includes positive and negative numbers, whole numbers, fractions, and decimals.
To add or subtract fractions, they must first be converted to have a common denominator. This is done by finding the least common multiple of the denominators and using it as the new common denominator.
Multiplying and dividing fractions follows simple rules: for multiplication, multiply the numerators and multiply the denominators; for division, keep the first fraction the same, change the division symbol to multiplication, and flip the second fraction.
Rational numbers
This document discusses two methods but provides no details about them. It appears to be comparing Method I and Method II but no information is given about what each method entails or their differences. The document does not contain enough information to summarize in 3 sentences or less.
Rational Numbers PPT
This document contains notes from a mathematics class taught by Soumya.S at Fatima Memorial Training College. The notes cover several topics:
1) Integers and rational numbers, defining integers as numbers that can be written without fractions and rational numbers as numbers that can be written as integers or fractions.
2) Rational expressions and how any rational number can be written as a fraction.
3) Different forms of rational expressions using the same rational number with different variables.
4) Operations including addition, subtraction, multiplication, and division of rational expressions.
Practical geometry for class 8th
This document discusses how to construct quadrilaterals given certain measurements. It provides examples of constructing quadrilaterals when given: 1) four sides and one diagonal, 2) two diagonals and three sides, 3) two adjacent sides and three angles, 4) three sides and two included angles, and 5) other special properties. Step-by-step instructions and diagrams are used to demonstrate constructing specific quadrilaterals based on given measurements.
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.
Strategic Intervention Material (SIM) Mathematics-TWO-COLUMN PROOF
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.
Strategic Intervention Materials
This document provides an overview and activities on solving quadratic equations by factoring. It begins by defining quadratic equations and their standard form. Several activities are presented to practice identifying quadratic equations, rewriting them in standard form, and factoring trinomials of the form x^2 + bx + c. The final activity involves factoring quadratic equations to determine their roots. The document aims to build mastery of skills needed to solve quadratic equations using factoring techniques.
Geometry presentation
Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.
Geometry the congruence of triangles
The document discusses congruent triangles and different postulates that can be used to prove triangles are congruent. It states that triangles can be proved congruent without showing all three pairs of congruent sides and angles. It then provides examples of different postulates like AAS, SAS, and SSS that can be used to prove triangles congruent. It also discusses isosceles triangles and how if two isosceles triangles share a common base, the line segment joining their vertices will bisect the common base at a right angle.
Viewers also liked (18)
First Year Teacher Training (afternoon session)- Content
First Year Teacher Training (afternoon session)- Content
Strategic Intervention Material (SIM) Mathematics-TWO-COLUMN PROOF
Strategic Intervention Material (SIM) Mathematics-TWO-COLUMN PROOF
Similar to Congruence of triangle
Mathematics
Triangles are congruent if their corresponding angles and sides are equal. There are three postulates for triangle congruency: SSS (side-side-side), ASA (angle-side-angle), and SAS (side-angle-side). SSS states that if all three sides of one triangle are equal to those of another, the triangles are congruent. ASA states that if two angles and the included side of one triangle are equal to those of another, the triangles are congruent. SAS states that if a side and the included angle of one triangle are equal to those of another, the triangles are congruent.
GE 4.3 proving triangles congruent 12-2
This document discusses different methods for proving that triangles are congruent: SSS, SAS, ASA, AAS, and HL. It defines congruent polygons as having the same size and shape, meaning all corresponding sides are the same length and all corresponding angles have the same measure. The order of letters in a congruence statement indicates which angles or sides are being shown as congruent to prove the triangles are congruent.
Triangles
This document summarizes key concepts in geometry related to triangles. It discusses similarity criteria including AAA, SSA, and SSS. It also covers the area theorem, Pythagorean theorem, and its converse. The basic proportionality theorem and its converse are explained as well as how they relate to parallel lines. In summary, this document outlines important triangle properties and theorems for understanding similarity, area, right triangles, and parallel lines.
Triangles
This document discusses various theorems and properties related to triangles. It explains the Basic Proportionality Theorem, also known as Thales' Theorem, which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. It also covers similarity criteria like AAA, SSA, and SSS. The Area Theorem demonstrates that the ratio of areas of similar triangles equals the square of the ratio of corresponding sides. Additionally, it proves Pythagoras' Theorem, which relates the sides of a right triangle, and its converse. In summary, the document outlines key triangle theorems regarding proportional division, similarity, areas, and the Pythagorean relationship between sides.
Triangles recaptulation.pptx
This document discusses similarity and congruency of triangles. It defines similarity as two polygons having equal corresponding angles and proportional corresponding sides. Congruency requires equal corresponding sides and angles. The document outlines three criteria for similarity: AAA, SSS, and SAS. It also covers the basic proportionality theorem, areas of similar triangles being proportional, and how Pythagoras' theorem relates to right triangles being similar.
Triangles
The document discusses different types of triangles based on the lengths of their sides: equilateral triangles have all three sides equal; isosceles triangles have two equal sides; scalene triangles have no equal sides. It also describes criteria for determining if two triangles are congruent, including side-angle-side (SAS), angle-side-angle (ASA), and side-side-side (SSS). Properties of triangles are outlined, such as the angle sum property that the interior angles sum to 180 degrees and the exterior angle property relating an exterior angle to the two interior angles. The Pythagorean theorem relating the sides of a right triangle is presented along with Heron's formula for calculating the area of any triangle.
Similarity of Triangles
This document discusses how to prove that two triangles are similar. It provides three conditions to show similarity: SSS, where the ratios of all three pairs of corresponding sides are equal; AAA, where two or more pairs of corresponding angles are equal; and SAS, where the ratios of two pairs of corresponding sides are equal and the included angles are also equal. Examples are given for each condition to demonstrate how to check if two triangles are similar.
An introduction to Congruent Triangles
This document discusses congruent triangles and their properties. It provides real-world and mathematical examples of congruent figures. The four main theorems for proving triangles are congruent are presented: SSS, ASA, SAS, and RHS. An example problem demonstrates using the RHS theorem to prove two triangles are congruent based on having equal bases and altitudes.
Congruence of Triangles
For class 7 mathematics.
Concepts are provided by M MAB ® Learning.
Questions try yourself.
Free notes download.
Ncert++ concepts.
Website: https://sites.google.com/view/m-mab/home
******
01 triangle new
1) The document discusses congruent figures and triangles. It defines congruent figures as those with the same shape and size that can be placed directly on top of each other.
2) It explains that triangles are congruent if their three sides or three angles are equal, or if one side and the two angles adjacent to it are equal.
3) It provides examples of congruent and non-congruent triangles based on different combinations of equal sides and angles.
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.
Triangles
Triangles can be classified based on side lengths as equilateral, isosceles, or scalene triangles. They can also be classified based on angles as acute, obtuse, or right triangles. The three main properties of triangles are the angle sum property, exterior angle property, and Pythagorean theorem. Congruent triangles can be proven using the SSS, SAS, ASA, AAS, or RHS criteria which compare corresponding sides and angles. Important parts of a triangle include the median, altitude, angle bisector, and perpendicular bisector. The triangle inequality states that the sum of any two sides must be greater than the third side. Important points related to triangles are the incenter, circumcenter,
Similar triangles
Two geometrical figures are similar if one can be obtained from the other by a uniform scaling (enlarging or shrinking) while maintaining the same shape. Specifically, two polygons are similar if they have the same corresponding angles and proportional side lengths, and two triangles are similar if they have the same three angles. The similarity of figures is denoted with a tilde symbol such as ΔABC ~ ΔDEF for similar triangles.
Similar Triangles or Triangle Similarity
This document discusses similar triangles and their properties. It begins with an opening prayer and review of past lessons. Then it presents an activity to play a "Try Not to Laugh" game in groups and earn additional points for a quiz. The objectives are presented, which are to investigate properties of similar triangles using ratios and proportions, compare similar and congruent triangles, and prove conditions of similarity. It defines similar triangles as those with the same shape but varying sizes, having equal corresponding angles and proportional corresponding sides. It presents the AA, SAS and SSS similarity theorems and examples. Properties, formulas and a comparison of similar and congruent triangles are discussed. An activity is assigned to identify given triangles as AA, SAS or SSS similar
Triangles
There are two main ways to classify triangles: by the lengths of their sides and by the measure of their angles. For side classification, an equilateral triangle has all three sides the same length, an isosceles triangle has two sides of equal length, and a scalene triangle has all sides of different lengths. For angle classification, an acute triangle has all angles less than 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and a right triangle has one 90 degree angle. Triangles can be proven congruent through various postulates and theorems including SSS, SAS, ASA, AAS, and RHS which relate congruent sides and angles.
Triangles
This document discusses several geometry theorems:
- The Basic Proportionality Theorem (also known as Thales' Theorem) states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
- There are four similarity criteria: AAA, SAS, SSS, and ASA, which define conditions for when two triangles are similar.
- The Area Theorem states that the ratio of the areas of similar triangles equals the square of the ratio of their corresponding sides.
- Pythagoras' Theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Triangles
1) A triangle is a three-sided polygon with three vertices and three edges.
2) Triangles can be classified based on side lengths (equilateral, isosceles, scalene) or interior angles (right, acute, obtuse).
3) The interior angles of any triangle always sum to 180 degrees. Congruent triangles have the same shape and size, while similar triangles have the same angle measures but sides proportional in length.
Quadrilaterals project
The document defines properties and methods to prove different types of quadrilaterals. It discusses properties and proofs for parallelograms, rectangles, kites, rhombuses, squares, and isosceles trapezoids. Key properties include opposite sides being parallel and congruent for parallelograms, right angles for rectangles, perpendicular diagonals for kites, and congruent angles and sides for squares. Methods of proof involve showing opposite sides are parallel/congruent, diagonals bisect each other, or angles are right or congruent.
6.3 terms
This document outlines five theorems that can prove if a quadrilateral is a parallelogram: if both pairs of opposite sides are congruent; both pairs of opposite angles are congruent; an angle is supplementary to both of its consecutive angles; the diagonals bisect each other; or one pair of opposite sides are congruent and parallel. It also summarizes the key properties of a parallelogram - both pairs of opposite sides are parallel and congruent, both pairs of opposite angles are congruent, or the diagonals bisect each other.
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
- A trapezoid is a quadrilateral with one pair of parallel sides called the bases. The non-parallel sides are called the legs.
- An isosceles trapezoid has one pair of parallel sides and one pair of congruent non-parallel sides called legs.
- Theorems about the isosceles trapezoid include: the base angles are congruent, opposite angles are supplementary, and the diagonals are congruent.
- The median of any trapezoid is parallel to the bases and is equal to half the sum of the bases.
Similar to Congruence of triangle (20)
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
Trapezoid-and-Isosceles-Trapezoid-Theorems-6-9-1 (1).pdf
More from Sai Sathvick Chirakala
Characteristics of healthy personality
Characteristics of healthy personality
TRAITS OF HEALTHY PERSONALITY
WAYS TO FEEL GOOD ABOUT YOURSELF
My Sql
This document provides examples of SQL queries based on various tables. It includes 15 sections with sample tables and SQL queries to retrieve information from those tables. The queries cover basic selects, filters, sorting, grouping, aggregation and other SQL operations. The document is a good reference for learning different types of SQL queries that can be written on various table structures.
Mysql and html
This document contains SQL queries and HTML code. The SQL section includes 16 queries on an EMP table with sample data. Queries retrieve and filter employee data by name, salary, department, hire date and more. The HTML section includes one form with fields to collect a user's name, password, country, computer type, comments and a submit button.
informatics practices practical file
This document contains 15 questions and answers related to Java programming. Each question asks the student to design a Java program to perform a specific task such as printing a table of numbers, calculating a Fibonacci series, or checking if a string is a palindrome. For each question, the student provides the code needed to solve the problem along with screenshots of a sample program preview and output.
content of cold drinks available in the market-chemistry investigatory project
content of cold drinks available in the market-chemistry investigatory projectSai Sathvick Chirakala
This chemistry project analyzes the contents of four popular cold drink brands - Coca Cola, Sprite, Limca, and Fanta. Through qualitative chemical tests, the student found that all drinks contained glucose, alcohol, sucrose, phosphate ions, and carbon dioxide. The pH levels varied between brands, with Coca Cola being the most acidic. Specifically, Sprite was found to have the maximum amount of dissolved carbon dioxide while Fanta had the minimum. In conclusion, while the drinks contained the same basic components, the amounts varied in each brand.Physics project class 12 EMI
The document describes an experiment on Faraday's law of electromagnetic induction. It includes an aim to determine the law using a copper wire, iron rod and magnet. It also includes sections on the certificate, acknowledgement, apparatus, introduction explaining the theory behind electromagnetic induction discovered by Faraday and Henry. The theory section defines magnetic flux and describes Faraday's law that the induced electromotive force in a closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit. It concludes that Faraday's law has many applications and impacts our lives in powering technologies.
02 chapter 11 thermodynamics
Here are the key steps to solve this problem:
1) Mass of coke = Volume x Density = 335 ml x 1 g/ml = 335 g
2) Temperature change = Room temperature (assume 70°F) - Coke temperature (35°F) = 70°F - 35°F = 35°F
3) Heat required to change temperature of coke = Mass x Heat capacity x Temperature change
= 335 g x 1 cal/g°C x 35°F/°C
= 335 x 1 x 35 = 11,725 cal
4) Convert calories to Joules: 11,725 cal x 4184 J/cal = 49,000 J
So the number
Chapter 11 equilibrium lecture notes
[CO2] = 0.4 - 2(4.3x10-3) = 0.396 mol/L
[CO] = 2(4.3x10-3) = 8.6x10-3 mol/L
[O2] = 4.3x10-3 mol/L
Class ion exchange 22 oct 08
Ion exchange chromatography can be used to separate metal ions. Ion exchange resins are polymer beads that contain ion exchange sites on their surface. Metal ions in solution can exchange with ions on the resin sites. There are cation exchange resins containing acidic sites that absorb positively charged metal ions and anion exchange resins containing basic sites that absorb negatively charged metal ion complexes. The affinity of metal ions for the resin depends on factors like the metal's charge and acid concentration. Ion exchange chromatography allows for sensitive separations of metals that are difficult to separate by other methods.
The frog and the nightingle
This poem tells the story of a frog who boasts of his singing abilities. One night, a nightingale sings beautifully and captivates the audience. The frog then offers to train the nightingale to improve her singing. He pushes her relentlessly through grueling practice sessions. The nightingale's singing becomes tired and unhappy. Eventually, the pressure causes the nightingale to have a fatal burst vein while singing. The frog concludes the nightingale was too weak, while he continues singing proudly in the bog.
More from Sai Sathvick Chirakala (10)
content of cold drinks available in the market-chemistry investigatory project
content of cold drinks available in the market-chemistry investigatory project
Congruence of triangle
- 1. TRIANGLES ISOSCELES EQUILATERAL TRIANGLES TRIANGLES SCALEN TRIANGLES
- 2. CONGRUENT FIGURES : CONGRUENT FIGURES ARE THE FIGURES WHICH HAVE EQUAL SIZE AND SHAPE IN SUCH A WAY THAT IF IT IS COVERED BY AN OTHER PAIR OF SAME FIGURE OVER IT THEY COVER EACH OTHER COMPLETELY. SIMILARLY, A TRIANGLE OF SAME SIZE AND SHAPE COVERS AN OTHER TRIANGLE OF SAME MEASUREMENTS IS KNOWN TO BE A CONGRUENCE OF TRIANGLES .
- 3. 50 50 4 cm 4 cm This is the first criterion for congruence of triangles. SAS Congruence rule: Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.
- 4. 60 45 60 45 4 cm 4 cm ASA Congruence Rule: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle .
- 5. 4 cm 4 cm SSS Congruence rule: If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
- 6. 4 cm 4 cm RHS Congruence rule: If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle are congruent. Right angle= hypotenuse-side