Congruent triangles
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Es una presentación del Profesor Jim Smith sobre congruencia de triángulos muy didáctica. Viene en idioma inglés.
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The document discusses several theorems and properties for proving when two lines are parallel, including:
1) If corresponding angles formed by a transversal intersecting two lines are congruent, then the lines are parallel.
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The document discusses several theorems and properties for proving when two lines are parallel, including:
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For class 7 mathematics.
Concepts are provided by M MAB ® Learning.
Questions try yourself.
Free notes download.
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This document provides information on proving triangle congruence using various postulates and properties. It discusses the six corresponding parts used to determine if two triangles are congruent, as well as five postulates for proving congruence: SSS, SAS, ASA, SAA/AAS, and the third angle theorem. Examples are given of applying each postulate, along with exercises to identify the postulate used and complete triangle congruence proofs. Key details include identifying the six corresponding parts of triangles as sides and angles, discussing the five postulates for proving congruence based on sides and angles, and providing examples of setting up triangle congruence proofs.
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.
lesson-1-congruent-triangles-v3-030919.pptx
The document discusses congruence of shapes and triangles. It defines congruence as two shapes being the same size and shape, and may be reflections or rotations of each other. There are four ways to prove triangles are congruent: side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and right-angle-hypotenuse-side (RHS). It provides examples of determining if given information is sufficient to prove triangles congruent and identifies the applicable congruence test. All shapes in the initial problem are congruent through rotations, reflections, and translations.
Ch 6 Ex 6.2
This document discusses triangles and similarity. It provides examples of using the AAA, SAS, and SSS similarity criteria to determine if two triangles are similar. It also contains exercises involving applying similarity rules to pairs of triangles and finding missing angle measures. One exercise involves showing two triangles are similar using the fact that corresponding angles are equal for diagonals intersecting in a trapezium where the bases are parallel. The summary is provided in 3 sentences or less as requested.
Ch 6 ex 6.2
This document discusses triangles and similarity. It provides examples of using the AAA, SAS, and SSS similarity criteria to determine if two triangles are similar. It also contains exercises involving applying similarity rules to pairs of triangles and finding missing angle measures. One exercise involves showing two triangles are similar using the fact that corresponding angles are equal for diagonals intersecting in a trapezium where the bases are parallel. The summary is provided in 3 sentences or less as requested.
Triangles
The document discusses different types of triangles and the properties used to determine if two triangles are congruent. It defines triangles and their components like sides and angles. It then explains the different types of triangles based on side lengths and angle measures. The properties used to prove triangle congruence are side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and hypotenuse-side (RHS).
Welcome To Geometry
This document introduces key concepts in geometry, including points, lines, planes, angles, polygons, triangles, quadrilaterals, and different types of geometric shapes. It defines important vocabulary like parallel lines, intersecting lines, perpendicular lines, acute angles, right angles, and obtuse angles. It also explains how to classify triangles based on angle types (right, acute, obtuse) and side lengths (scalene, isosceles, equilateral). Similarly, it describes how to classify quadrilaterals such as parallelograms, rectangles, rhombi, squares, and trapezoids based on their properties.
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.
E-RESOUCE BOOK
The document contains information about triangles, including:
1) If two triangles have proportional sides and equal angles, they are similar triangles.
2) In a right triangle, a perpendicular line from the right angle to the hypotenuse divides it into two right triangles that are similar to each other and to the original triangle.
3) A line dividing two sides of a triangle proportionally is parallel to the third side.
QUARTER-3-GRADE-8-WEEK-3.pptx
This document discusses triangles and triangle congruence. It defines different types of triangles based on side lengths and angle measures. It also defines congruent figures and introduces the triangle congruence postulate. Properties of triangle congruence such as reflexive, symmetric, and transitive properties are presented. The document explains how to prove triangles are congruent by showing corresponding parts are congruent. It also discusses angle sums in triangles and side-angle relationships in triangles.
Geometry toolbox advanced proofs (3)
The document provides definitions and properties related to geometry concepts like angles, triangles, quadrilaterals, and their various parts. It contains cards that can be clicked on to review postulates, definitions, algebraic properties, theorems about angles, triangles, quadrilaterals, and their angle and segment relationships. The purpose is to provide resources for justifying conclusions using the geometric rules and concepts learned.
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Congruent triangles
- 2. When we talk about congruent triangles, we mean everything about them Is congruent. All 3 pairs of corresponding angles are equal…. And all 3 pairs of corresponding sides are equal
- 3. For us to prove that 2 people are identical twins, we don’t need to show that all “2000” body parts are equal. We can take a short cut and show 3 or 4 things are equal such as their face, age and height. If these are the same I think we can agree they are twins. The same is true for triangles. We don’t need to prove all 6 corresponding parts are congruent. We have 5 short cuts or methods.
- 4. SSS If we can show all 3 pairs of corr. sides are congruent, the triangles have to be congruent.
- 5. SAS Show 2 pairs of sides and the included angles are congruent and the triangles have to be congruent. Included angle Non-included angles
- 6. This is called a common side. It is a side for both triangles. We’ll use the reflexive property.
- 7. Which method can be used to prove the triangles are congruent
- 8. Common side SSS Parallel lines alt int angles Common side SAS Vertical angles SAS
- 10. ASA, AAS and HL A ASA – 2 angles and the included side AAS – 2 angles and The non-included side S A A A S
- 11. HL ( hypotenuse leg ) is used only with right triangles, BUT, not all right triangles. HL ASA
- 12. When Starting A Proof, Make The Marks On The Diagram Indicating The Congruent Parts. Use The Given Info, Properties, Definitions, Etc. We’ll Call Any Given Info That Does Not Specifically State Congruency Or Equality A PREREQUISITE
- 13. SOME REASONS WE’LL BE USING • • • • • • DEF OF MIDPOINT DEF OF A BISECTOR VERT ANGLES ARE CONGRUENT DEF OF PERPENDICULAR BISECTOR REFLEXIVE PROPERTY (COMMON SIDE) PARALLEL LINES ….. ALT INT ANGLES
- 14. A C B 1 2 E SAS Given: AB = BD EB = BC Prove: ∆ABE = ∆DBC ˜ Our Outline P rerequisites D S ides A ngles S ides Triangles = ˜
- 15. A 1 E P S A S ∆’s C B 2 SAS D STATEMENTS none AB = BD 1=2 EB = BC ∆ABE = ∆DBC ˜ Given: AB = BD EB = BC Prove: ∆ABE = ∆DBC ˜ REASONS Given Vertical angles Given SAS
- 16. C 12 Given: CX bisects ACB A= B ˜ Prove: ∆ACX = ∆BCX ˜ AAS A X B P CX bisects ACB A 1= 2 A A= B S CX = CX ∆’s ∆ACX = ∆BCX ˜ Given Def of angle bisc Given Reflexive Prop AAS
- 17. Can you prove these triangles are congruent?
Editor's Notes
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