Question

In the adjoining figure ,AB congruent CD.Prove that angle A=angle B​

Answer 1

Answer:

∠A = ∠B

Explanation:

Given: arc AB = arc CD

To prove: ∠A = ∠B.

Proof:  

In ∆AOC and ∆BOD, OA = OB = OC = OD. (radius of the circle)

Since ∆AOC and ∆BOD are an isosceles triangles, ∠A = ∠C and ∠B = ∠D. (Base angles of an isosceles triangle).

Also in ∆BOC, OB = OC (radius), so base angles ∠B = ∠C.

So all two sides and two angles are equal between the triangles ∆AOC and ∆BOD.

So  ∆AOC is congruent to ∆BOD.

Hence the corresponding angles of the two triangles will be equal.

So ∠A = ∠B. Hence proved.

Answer 2

Answer:

∠A = ∠B

Explanation:

Given: arc AB = arc CD

To prove: ∠A = ∠B.

Proof:  

In ∆AOC and ∆BOD, OA = OB = OC = OD. (radius of the circle)

Since ∆AOC and ∆BOD are an isosceles triangles, ∠A = ∠C and ∠B = ∠D. (Base angles of an isosceles triangle).

Also in ∆BOC, OB = OC (radius), so base angles ∠B = ∠C.

So all two sides and two angles are equal between the triangles ∆AOC and ∆BOD.

So  ∆AOC is congruent to ∆BOD.

Hence the corresponding angles of the two triangles will be equal.

So ∠A = ∠B. Hence proved.