100 likes | 197 Views
4.2 Congruence and Triangles. Identify congruent figures and corresponding parts. Prove that 2 triangles are congruent. Congruence and Correspondence.
E N D
4.2 Congruence and Triangles Identify congruent figures and corresponding parts Prove that 2 triangles are congruent
Congruence and Correspondence • When 2 figures are congruent there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.
Z • If Δ ABC is to Δ XYZ, which angle is to C?
3rd Angles Theorem • If two ’s of one triangle are to two ’s of another triangle, then the third ’s are also .
Example: find x ) ) 22o )) 87o )) (4x+15)o
Example: Continued 22+87+4x+15=180 4x+15=71 4x=56 x=14
Ex: ABCD is to HGFE, find x and y. F E 9cm B (5y-12)o A 91o 86o H G 113o 4x-3cm D C 4x-3=9 5y-12=113 4x=12 5y=125 x=3 y=25
Properties of Congruent Triangles(Theorem 4.4) 1. Reflexive: 2. Symmetric: 3.Transitive:
Writing a Congruence Statement D C A B F E