Question

Show that in an isosceles triangle, the angle opposite to equal sides
are equal. (Hint: Draw perpendicular bisector of unequal side)​

Answer 1

Visualisation:

Draw a ∆ABC

Answer:

Given:ABC is an isosceles triangle i.e., AB=AC

To prove: Angles opposite to equal sides are equal i.e.,B=C

Construction: Draw a median AD to the side BC of ∆ABC.

Consider ∆ABD and ∆ACD,

AB=AC (Given)

AD=DA (Common)

BD=CD (Construction)

By SSS congruency rule,

∆ACD is congruent to ∆ABD

By CPCT,

B=C

Thus,angles opposite to equal sides are equal

Hence,proved

Answer 2

angles opposite to equal

hence proved