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4.2 Congruence and Triangles • Two geometric figures are congruent if they have exactly the same size and shape. • When two figures are congruentcorresponding angles are congruent and corresponding sides are congruent. ABC =̃ PQR B Q A C P R mA mP mB mQ BC QR mC mR CA RP AB PQ 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 E B D A ABC=̃ EFD C F • Given M =̃ G and N =̃ H, find the value of x. H M 142° N J P G X=32 More Practice Problems Given that N =̃ R and L =̃ S, find the value of x. M R N 55° 65° L S (2X+30)° T X=15 Given that LMN =̃ answer the following: PQR, P N Q 45° R L mP= 105° mM= 45° mR= 30° mN= 30° 105° QR =̃ MN LN =̃ PR M Identify any figures that can be proved congruent. If congruent, write a congruence statement. A B C D