Question

Prove that, angles opposite to equal sides of an isosceles triangle are equal.​

Answer 1

Answer: So your answer is

Step-by-step explanation:

Given: In the isosceles ∆XYZ, XY = XZ.

To prove ∠XYZ = ∠XZY.

Construction: Draw isosceles ΔXYZ. Draw a line XM such that it bisects ∠YXZ and meets the side YZ at M.

Proof:                  1. In ∆XYM and ∆XZM,

                    (i) XY = XZ  (Given)

                   (ii) XM = XM   (Common side)

                    (iii) ∠YXM = ∠ZXM   (XM bisects ∠YXZ)

                           2. ∆XYM ≅ ∆XZM    (By SAS criteria)

                           3. ∠XYZ = ∠XZY. (Proved)      (BY CPCT)