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3.7 Angle-Side Theorems Objectives: Apply theorems relating the angle measures and the side lengths of triangles.

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Presentation on theme: "3.7 Angle-Side Theorems Objectives: Apply theorems relating the angle measures and the side lengths of triangles."— Presentation transcript:

1 3.7 Angle-Side Theorems Objectives: Apply theorems relating the angle measures and the side lengths of triangles

2 Theorem: If two sides of a triangle are congruent, then the opposite angles are congruent. Theorem: If two angles of a triangle are congruent, then the opposite sides are congruent. A B C R S T

3 Theorem: If two sides of a triangle are congruent, then the opposite angles are congruent. Theorem: If two angles of a triangle are congruent, then the opposite sides are congruent. How do you prove triangles are isosceles? 1.Prove at least two sides congruent. 2.Prove at least two angles congruent.

4 Based on these last theorems, what conclusions can be drawn about equilateral and equiangular triangles? A B C X Y Z

5 Theorem: If two sides of a triangle are not congruent, then the opposite angles are not congruent and the larger angle is opposite the longer side. Theorem: If two angles of a triangle are not congruent, then the opposite sides are not congruent and the longer side is opposite the larger angle. A C B Z Y X

6 F E D Example 1: List the sides from least to greatest. 24° 46° 110°

7 N L M 13 Example 2: List the angles from least to greatest. 12 5

8 Example 3: StatementsReasons 1. 2. 3. Definition of isosceles Given All radii of a circle are congruent L M N K

9 Example 4: StatementsReasons 1. 2. 3. 4. 5. 6. 7. 8. 9. Linear Pair Postulate Given Linear Pair Postulate F I G H J L K 21 Congruent Supplements Thm. Given SAS Given CPCTC Definition of isosceles

10 Example 4: StatementsReasons 1. 2. 3. 4. 5. 6. 7. Definition of isosceles Given Definition of isosceles Given Addition Property Reflexive Property SAS F A E B D

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