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Question

State true or false:
The following figure shows a trapezium ABCD in which ABDC. P is the mid-point of AD and PRAB.
Hence,
PR=12(AB+CD)

178847.JPG

A
True
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B
False
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Solution

The correct option is A True
In , BDC and BQR,
B=B (Common)
BDC=BQR (Corresponding angles of parallel lines)
BCD=BRQ (Corresponding angles of parallel lines)
thus, BDCBQR
Thus, BDQB=DCQR
2=DCQR (Q is the mid point of BD)
QR=12DC
Similarly, QP=12AB
Hence, QR+QP=12(AB+DC)
PR=12(AB+CD)

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