Question

Assertion : ABCD and PQRC are rectangles and Q is 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.
Which of the following is correct?

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

Answer 1

The correct option is B

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

In $\Delta ADC$, 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 correct explanation of assertion.