Question

prove that angles opposite to the the equal sides of an isosceles triangle are equal​

Answer 1

Answer:

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

 

To prove ∠XYZ = ∠XZY.

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

Proof:

         Statement

1. In ∆XYM and ∆XZM,

(i) XY = XZ

(ii) XM = XM

(iii) ∠YXM = ∠ZXM

2. ∆XYM ≅ ∆XZM

3. ∠XYZ = ∠XZY. (Proved)

         Reason

1.

(i) Given.

(ii) Common side.

(iii) XM bisects ∠YXZ.

2. By SAS criterion.

3. CPCTC.

Step-by-step explanation:

Answer 2

Answer:

Thus we can say that ΔBAD is equal to ΔCAD, by SAS congruent rule, where 2 sides and one angle of one triangle is equal to 2 sides and one angle of another triangle. Thus we can say that ∠ABD is equal to ∠ACD, as both triangles are equal. Hence we proved that the angles opposite to equal sides are equal

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