Lesson 6.7 Congruent Triangles pp. 245-250.

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Presentation transcript:

Lesson 6.7 Congruent Triangles pp. 245-250

Objectives: 1. To prove the Side-Angle-Angle Theorem for triangles. 2. To prove the Isosceles Triangle Theorem. 3. To use these theorems to prove other theorems about congruent triangles.

Theorem 6.19 SAA Congruence Theorem. If two angles of a triangle and a side opposite one of the two angles are congruent to the corresponding angles and side of another triangle, then the two triangles are congruent.

C Z A B X Y

Theorem 6.20 Isosceles Triangle Theorem. In an isosceles triangle the two base angles are congruent.

Theorem 6.21 If two angles of a triangle are congruent, then the sides opposite those angles are congruent, and the triangle is an isosceles triangle.

Theorem 6.22 A triangle is equilateral if and only if it is equiangular.

Homework pp. 248-250

1. Find the measure of each angle. ►A. Exercises 1. Find the measure of each angle. A B C 20°

►A. Exercises 2. Find the measure of each angle.

3. Find the measure of each angle. ►A. Exercises 3. Find the measure of each angle. Q P R x x-15

4. Find the measure of each angle. ►A. Exercises 4. Find the measure of each angle. U T V 110°

11-15. L N M P O Q 1 2 3 4

■ Cumulative Review 22. Review the proof of Theorem 6.20. What rule of logic enables us to apply the reflexive property to step 4?

■ Cumulative Review 23. Name at least three of the equivalence relations you have studied so far.

■ Cumulative Review 24. Given: AD || BC; 1  3 Prove: ABC  ACB A

■ Cumulative Review Let P represent a point and l and m lines.  l   P  l  m so that m || l  P  m 25. Write the symbolic statement as a sentence. Do you recognize it?