Question

In the given figure, if $O$ is the midpoint of AB and CD, then which of the following must be true?

• A. $AC=BD$
• B. $AC||BD$
• C. Both (a) & (b)
• D. $AC=OA$

Answer 1

The correct option is C Both (a) & (b)



In $\Delta AOC$ and $\Delta BOD$,
$AO=OB$ (given)
$CO=OD$ (given)
$\angle 1=\angle 2$ (Vertically opp. angles)
$\therefore \Delta AOC\cong \Delta BOD$ (by SAS congruence criterion)
$\angle OAC=\angle OBD$
$\angle OCA=\angle ODB$ (CPCT)
these are alternative interior angles
$\Rightarrow AC||BD$
Here, we cannot prove $AC=OA$
So, the correct answer is option (c).