MCQ
In the adjoining figure, $O$ is Mid–point of $AB$. If $\angle\text{ACO} = \angle\text{BDO},$ then $\angle\text{OAC}$ is equal to:
- A$\angle\text{BOD}$
- B$\angle\text{OCA}$
- C$\angle\text{ODB}$
- ✓$\angle\text{OBD}$
✓
Answer
Correct option: D.
$\angle\text{OBD}$
In $\triangle\text{OAC}$ and $\triangle\text{OBD},$
$AO = OB$ As $O$ is the mid-point of $AB$
$\triangle\text{AOC}=\ \triangle\text{BOD}$ (Vertically Opposite Angles)
$\triangle\text{AOC}=\ \triangle\text{BDO}$ (Given)
$\therefore\ \triangle\text{OAC}=\ \triangle\text{OBD}$ ($AAS$ Axiom)
$\therefore\ \triangle\text{OAC}=\ \triangle\text{OBD}$ $(C.P.C.T.)$
$AO = OB$ As $O$ is the mid-point of $AB$
$\triangle\text{AOC}=\ \triangle\text{BOD}$ (Vertically Opposite Angles)
$\triangle\text{AOC}=\ \triangle\text{BDO}$ (Given)
$\therefore\ \triangle\text{OAC}=\ \triangle\text{OBD}$ ($AAS$ Axiom)
$\therefore\ \triangle\text{OAC}=\ \triangle\text{OBD}$ $(C.P.C.T.)$
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