Question

show that in an isosceles triangle the angles opposite to the equal sides are equal ................​

Answer 1

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.

Answer 2

Answer:

hey my cute friend your answer is here.............

Given =A triangle ABC in which AB=AD ..............

To Prove=angleB=angleC..........

Construction =AD perpendicular to BC.............

Proof = in the right triangles ADB and ADC, we have :

hypotenuse AB = hypotenuse AC (given) and side AD=side AD (common) .........

hence triangle ADB congruent to triangle ADC (RHS congruence property)............

hence proved angle B = angle C.............

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