question_answer

In \[\Delta ABC,\] P and Q are the midpoints of AB and AC. If PQ is produced to R such that \[PQ=QR,\]what is PRCB?

A)  A rectangle  

B)                         A square

C)                         A rhombus  

D)                         A parallelogram

Correct Answer: D

Solution :

Since P and Q are mid points of AB and AC, \[PQ=\frac{1}{2}BC\]and \[PQ||BC\]. So, \[BC=2PQ=PR\] Hence, PRCB is a parallelogram.