Question

show that in an isoscale triangle ,angle opposite to equal side are equal.​

Answer 1

≡QUESTION≡

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

                                                       

║⊕ANSWER⊕║

Given - An isosceles Δ ABC

            AB=AC

To prove :- Angles opposite to equal sides are also equal

Construction :- Draw AP bisector of angle A meeting BC at P.

In ∆ABP and ∆ACP

AP=AP[common]

AB=AC [given]

∠ BAP = ∠ CAP [by construction]

∴ ∆ABP ≅ ∆ACP [S.A.S]

∴ ∠ABP = ∠ACP [C.P.C.T]

Hence proved that angles opposite to equal sides of a triangle are equal.