State whether the following is true or false.

If ABCD and BPQR are two rectangles and $Q$ is the mid-point of the diagonal AC, then $PR = \frac{1}{2} AC$ .

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True

False

answer is A.

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Detailed Solution

Given two rectangles ABCD and BPQR, Q is midpoint of BD.
Question Image

In ΔACD,
Q is mid -point of AC and QP || AD (Sides of rectangle)
∴ P is mid-point of CD
∴ DP = PC
∵ PR and QC are the diagonals of rectangle PQRC,
∴ PR = QC
But Q is the mid-point of AC
∴QC=

\frac{1}{2}

AC
Hence PR=

\frac{1}{2}

AC.
Thus, if ABCD and BPQR are two rectangles and

Q

is the mid-point of the diagonal AC, then

PR = \frac{1}{2} AC

.
Therefore, option (1) is correct and the given statement is true.

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