Mathematics
In the adjoining figure, OA ⊥ OD, OC ⊥ OB, OD = OA and OB = OC. Prove that AB = CD.
Triangles
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Answer
From figure,
∠AOD = ∠COB (Each 90°)
Adding ∠AOC to both sides,
⇒ ∠AOD + ∠AOC = ∠AOC + ∠COB
⇒ ∠COD = ∠AOB.
Now, in △AOB and △DOC
OA = OD (Given)
OB = OC (Given)
∠AOB = ∠COD (Proved)
∴ △AOB ≅ △DOC (SAS axiom)
We know that corresponding parts of congruent triangles are equal.
∴ AB = CD.
Hence, proved that AB = CD.
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