Prove that two isosceles triangles are similar if any angle of one equals the corresponding angle of the other.Given: Isosceles\triangle ABC , isosceles △ DEF, AC = BC, DF = EF, ∠ C=∠ F, Prove: △ ABCsim△ DEF

Tamara Anthony

Tamara Anthony

Open question

2022-08-20

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: IsoscelesABC , isosceles DEF, AC=BC, DF=EF, C=F
Prove: ABCDEF
Statementc
1.(see above)
2.
3.ABCDEF
Reasons
1.Given
2. Isosceles triangles with equal vertex angles have equal base angles also.(ex. 2.14 #5)
3. ?

Answer & Explanation

Ben Reese

Ben Reese

Beginner2022-08-21Added 12 answers

Step 1
Given,
a.Casr 1:Equal Vertex Angles
Given: Isosceles ABC, isosceles DEF,AC=BC,DF=EF,C=F
Prove: ABCDEF
Step 2
Statements
1. C=F
2. A=D and B=E 
3. DECABC
Reasons
Given
Isosceles triangle with equal vertex angles have equal base angles also.
If two triangles have the three angles of one equal respectivelyto the three angles of the other,then the triangles are similar

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