Assertion: In ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP intersect BC at P and FE at Q. Then AQ = QP.
Reason: Q is the mid - point of AP.
Which of the following is correct?
The correct option is A: Both the assertion and the reason are true and the reason is the correct explanation for the assertion
In ΔABC, E and F are mid-point of sides AC and AB respectively. ∴FE∥BC [ mid-point theorem]
Now, in ΔABP, F is mid-point of AB and FQ∥BP
⇒ Q is mid-point of AP [a line drawn through the mid-point of one side of a triangle parallel to second side bisects the third side.]
⇒ AQ = QP