Question

In the given figure, AC and DB are perpendicular bisector of each other and AC = DB. Then

• A. $△$AOB $\cong$ $△$BOC $\cong$ $△$COD $\cong$ $△$DOA
• B. $△$AOB $\cong$ $△$BOC $≆$ $△$COD $\cong$ $△$DOA
• C. $△$AOB $\cong$ $△$BOC $\cong$ $△$COD $≆$ $△$DOA
• D. $△$AOB $\cong$ $△$BOC $≆$ $△$COD $≆$ $△$DOA

Answer 1

The correct option is A $△$AOB $\cong$ $△$BOC $\cong$ $△$COD $\cong$ $△$DOA

Since AC and DB are perpendicular bisector of each other , AC=DB
Therefore AO=BO=CO=DO
and,
$\angle$AOB = $\angle$ BOC = $\angle$COD = $\angle$DOA = ${90}^{\circ }$


Every triangle in the figure has two congruent sides and one right angle in common.
Therefore,
$△$AOB $\cong$ $△$BOC $\cong$ $△$COD $\cong$ $△$DOA are congruent by SAS criteria.