In the adjoining figure, O is Mid–point of AB. If = , then is equ… - Vidyadip

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)
$\therefore\ \triangle\text{OAC}=\ \triangle\text{OBD}$ $(C.P.C.T.)$

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