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Mathematics

In the adjoining figure, O is the mid-point of AB. If ∠ACO = ∠BDO, then ∠OAC is equal to

  1. ∠OCA

  2. ∠ODB

  3. ∠OBD

  4. ∠BOD

In the adjoining figure, O is the mid-point of AB. If ∠ACO = ∠BDO, then ∠OAC is equal to? Triangles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Triangles

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Answer

In △AOC and △BOD,

AO = OB (As O is the mid-point of AB.)

∠ACO = ∠BDO (Given)

∠AOC = ∠BOD (Vertically opposite angles)

Hence, △AOC ≅ △BOD by AAS axiom.

We know that corresponding parts of congruent triangles are equal.

∴ ∠OAC = ∠OBD.

Hence, Option 3 is the correct answer.

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