Question

Assertion: In $\Delta ABC$, E and F are the mid-points of AC and AB respectively. The altitude AP at BC intersect and FE at Q. Then AQ = QP.
Reason: Q is the mid - point of AP.
Which of the following is correct?

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

Answer 1

The correct option is A Both the assertion and the reason are true and the reason is the correct explanation for the assertion

In $\Delta ABC$, E and F are mid-point of sides AC and AB respectively.
$\therefore FE\parallel BC$ [ mid-point theorem]

Now, in $\Delta ABP$, F is mid-point of AB and $FQ\parallel BP$
$\Rightarrow$ Q is mid-point of AP
$\Rightarrow$ AQ = QP