Question

theorem : the sides opposite to equal angles of a triangle are equal prove this class 9

Answer 1

Answer:

Step-by-step explanation:

Given: In ∆ABC, ∠XYZ = ∠XZY.

To prove: XY = XZ

Construction: Draw the bisector XM of ∠YXZ so that it meets YZ at M.

Proof:

         Statement                                             Reason

1. In ∆XYM and ∆XZM,                         1.

(i) ∠XYM = XZM                                      (i) Given                          

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

(iii) XM = XM                                           (iii) Common side

2. ∆XYM ≅ ∆XZM                                  2. By AAS criterion.

3. XY = XZ. (Proved)                                3. CPCTC.

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