Question

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

Answer 1

Step-by-step explanation:

Let △ABC be an isosceles triangle such that AB =AC

Then we have to prove that ∠B=∠C

Draw the bisector AD of ∠A meeting BC in D

Now in triangles ABD and ACD

We have AB=AC (Given)

∠BAD=∠CAD (because AD is bisector of ∠A

AD=AD (Common side)

Therefore by SAS congruence condition we have

△ABC≅△ACD

⇒∠B=∠C

(Corresponding parts of congruent triangles are equal )