Question

Assertion: $ABCD$ and $PQRC$ are rectangles and $Q$ is the mid - point of $AC.$ Then $DP=PC.$

Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it.

• A. Both assertion and reason are true and reason is the correct explanation of assertion
• B. Both assertion and reason are true but reason is not the correct explanation of assertion
• C. Assertion is true but reason is false
• D. Assertion is false but reason is true

Answer 1

The correct option is B

Both assertion and reason are true but reason is not the correct explanation of assertion

In $△ADC,Q$ is the mid-point of $AC$ such that $PQ\parallel AD$
$\therefore P$ is the mid-point of $DC$
$\Rightarrow DP=PC$ [using converse of mid-point theorem]

$\therefore$ Assertion is true, reason is true but reason is not the correct explanation of assertion.