Prove that two isosceles triangles are similar if any angle of one equals the corresponding angle of the other. a. Case 1: Equal Vertex Angles Given: Isosceles△ ABC , isosceles △ DEF, AC = BC, DF = EF, ∠ C=∠ F Prove: △ ABC~ △ DEF Statementc 1.(see above) 2. 3.△ABC ~ △DEF Reasons 1.Given 2. Isosceles triangles with equal vertex angles have equal base angles also.(ex. 2.14 #5) 3. ?
Step 1 Given, a.Casr 1:Equal Vertex Angles Given: Isosceles △ ABC,Isosceles △ DEF,AC=BC,DF=EF,∠ C=∠ F Prove: △ ABC~ △ DEF Step 2 Statements 1. ∠ C=∠ F 2. ∠ A=∠ D and ∠ B =∠ E 3. △ DEC ~ △ ABC Reasons Given Isosceles triangle with equal vertex angles have equal base angles also. If two triangles have the three angles of one equal respectively to the three angles of the other,then the triangles are similar