Question

In the adjoining figure, $ABCD$ is a trapezium in which $AB\parallel DC$ and $P,Q$ are the midpoint of $AD$ and $BC$ respectively,$DQ$ and $AB$ when produced meet at $E$. Also ,$AC$ and $PQ$ intersect at $Q$, then $DQ=2QE$

• A. True
• B. False

Answer 1

The correct option is B False

In figure $△$QCD & $△$QBE

we know that $\angle$DQC and $\angle$BQE are vertically opposite angle

So we get,

$\Rightarrow \angle$DQC = $\angle$BQC

From the figure we know that $\angle$QDC and $\angle$QEB are alternate angle.

$\Rightarrow \angle$QDC = $\angle$QEB.

By ASA congruence criterion

$\Rightarrow △$QCD = $△$QBE

$\therefore$ DQ = QE

given statement DQ = 2 QE is false.

$\therefore$ It is false.