Question

state and prove isosceles triangle theorem


​

Answer 1

Step-by-step explanation:

Isosceles Triangle Theorem: If two sides of a triangle are congruent, then angles opposite those sides are congruent. ... If angles opposite those sides are congruent, then two sides of a triangle are congruent.

Answer 2

The Isosceles triangle theorem states that if two sides of a triangle are congruent, then angles opposite those sides are congruent.

Consider an isosceles triangle ABC where AC = BC.

Diagram are in the attachment

We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.

first draw a bisector of ∠ACB and name it as CD.

In ∆ACD and ∆BCD

AC = BC                                                   (Given)

∠ACD = ∠BCD                                     (By construction)

CD = CD                                                              

Thus,  ∆ACD ≅∆BCD                                        

So, ∠CAB = ∠CBA    

Hence prove isosceles triangle theorem