Assertion: In $Δ A B C$ , 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?

Both the assertion and the reason are true and the reason is the correct explanation for the assertion

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

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The assertion is true and the reason is false

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The assertion is false and the reason is true

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Solution

The correct option is A: Both the assertion and the reason are true and the reason is the correct explanation for the assertion
In $Δ A B C$ , E and F are mid-point of sides AC and AB respectively. $∴ F E ∥ B C$ [ mid-point theorem]

Now, in $Δ A B P$ , F is mid-point of AB and $F Q ∥ B P$

$\Rightarrow$ 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.]

$\Rightarrow$ AQ = QP

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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?

Assertion: In $Δ A B C$ , 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?