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. ?

1 Answers

Best Answer

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