4.2 Congruence and Triangles

4.2 Congruence and Triangles • Two geometric figures are congruent if they have exactly the same size and shape. • When two figures are congruentcorresponding angles are congruent and corresponding sides are congruent.

ABC =̃ PQR B Q A P R C

Third Angles Theorem • If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Properties of Congruent Triangles • Reflexive Property: Every triangle is congruent to itself. • Symmetric Property of Congruent Triangles: If ABC =̃ DEF, then DEF =̃ ABC • Transitive Property of Congruent Triangles: If ABC =̃ DEF and DEF =̃ JKL, then ABC =̃ JKL.

Practice Problems • Name the congruent figures • Given M =̃ G and N =̃ H, find the value of x. E B D ABC=̃ EFD A C F (2X-50)° H M 142° N J 24° P G X=32

R M S (2X+30)° L N 55° 65° T More Practice Problems Given that N =̃ R and L =̃ S, find the value of x. X=15

MN P N PR Q 45° R L 105° M Given that LMN =̃ PQR, answer the following: mP= QR =̃ mM= LN =̃ mR= mN= 105° 45° 30° 30°

C A D B Identify any figures that can be proved congruent. If congruent, write a congruence statement.

4.2 Congruence and Triangles