Congruence and Triangles 4-2 Congruence and Triangles Holt Geometry Warm Up Lesson Presentation Lesson Quiz

4.2 Congruence and Triangles Warm Up 1. Find the measure of exterior DBA of BCD, if mDBC = 30°, mC= 70°, and mD = 80°. 2. What is the complement of an angle with measure 17°? 3. How many lines can be drawn through N parallel to MP? Why? 150° 73° 1; Parallel Post.

4.2 Congruence and Triangles When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

4.2 Congruence and Triangles

Example 1: Proving Two Triangles are Congruent 4.2 Congruence and Triangles Example 1: Proving Two Triangles are Congruent

Example 1: Proving Two Triangles are Congruent 4.2 Congruence and Triangles Example 1: Proving Two Triangles are Congruent

4.2 Congruence and Triangles

Example 2: Applying the Third Angles Theorem 4.2 Congruence and Triangles Example 2: Applying the Third Angles Theorem Find mK and mJ. K  J Third s Thm. mK = mJ Def. of  s. 4y2 = 6y2 – 40 Substitute 4y2 for mK and 6y2 – 40 for mJ. –2y2 = –40 Subtract 6y2 from both sides. y2 = 20 Divide both sides by -2. So mK = 4y2 = 4(20) = 80°. Since mJ = mK, mJ = 80°.

4.2 Congruence and Triangles Check It Out! Example 2 Find mP and mT. P  T Third s Thm. mP = mT Def. of  s. 2x2 = 4x2 – 32 Substitute 2x2 for mP and 4x2 – 32 for mT. –2x2 = –32 Subtract 4x2 from both sides. x2 = 16 Divide both sides by -2. So mP = 2x2 = 2(16) = 32°. Since mP = mT, mT = 32°.

4.2 Congruence and Triangles Lesson Quiz I 1. Find mN and mP. 75°; 75°

4.2 Congruence and Triangles Lesson Quiz II 2. 105° 45° 30° 30° MN PR