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4. Show that in an isosceles triangle, angles opposite to equal sides are equal.​

Answer»

Answer:

Proof: Consider an isosceles triangle ABC where AC = BC.

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

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

Now in ∆ACD and ∆BCD we have,

AC = BC       (Given)

∠ACD = ∠BCD   (By construction)                                                  

CD = CD       (Common to both)                                                        

Thus,  ∆ACD ≅∆BCD  (By SAS congruence CRITERION)                                      

So, ∠CAB = ∠CBA       (By CPCT)                                        

Hence proved. In an isosceles triangle, angles opposite to equal sides are equal.​


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