In the following figure- if O A-O D and - 1- 2- Prove that - O C B is an isosceles triangle-

Given: OA = OD and ∠1=∠2 In ∆OCA nbsp;and nbsp;∆OBD OA = OD nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Standard IX

Mathematics

RHS Criteria for Congruency

In the follow...

Question

In the following figure, if OA = OD and $∠ 1 = ∠ 2$ . Prove that ΔOCB is an isosceles triangle.

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Solution

Given: OA = OD and $∠ 1 = ∠ 2$
In $∆ O C A and ∆ O B D$
OA = OD (Given)
$∠ A O C = ∠ D O B$ (Vertically opposite angles)
$∠ 1 = ∠ 2 (Given) \Rightarrow 180^{\circ} - ∠ 1 = ∠ 2 - 180^{\circ} \Rightarrow ∠ C A O = ∠ B D O$
$∴ ∆ C A O ≅ ∆ B D O$ (By ASA)
Thus, by corresponding parts of congruent triangles, we have
OC = OB
Hence, ΔOCB is an isosceles triangle.

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In the following figure, if OA = OD and ∠1=∠2. Prove that ΔOCB is an isosceles triangle.

In the following figure, if OA = OD and $∠ 1 = ∠ 2$ . Prove that ΔOCB is an isosceles triangle.