Question

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Prove that angles opposite to two equal sides of a triangle are equal.

Answer this question....

Answer 1

Prove that angles opposite equal sides are equal in a triangle. Consider ΔABC and draw median AD. Consider ΔABD and ΔCBD, AB = AC (Given that two sides of the triangle are equal.) BD = CD (AD is the median of the triangle) AD = AD (Common side) ∴ ΔABD ≅ ΔCBD (SSS congruency) ∴ ∠B = ∠C (Corresponding parts of congruent triangles) Hence, angles opposite to equal sides are equal in a triangle.

Answer 2

Take a triangle ABC, in which AB=AC.

Construct AP bisector of angle A meeting BC at P.

In ∆ABP and ∆ACP

AP=AP[common]

AB=AC[given]

angle BAP=angle CAP[by construction]

Therefore, ∆ABP congurent ∆ACP[S.A.S]

This implies, angle ABP=angleACP[C.P.C.T]

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