In the given figure, PQRS is a parallelogram. A and B are the mid-point of `bar(PQ)` and `bar(SR)` respectively. If PS=BR, then the quadrilateral ADBC is a…………………… ,
ltimg src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/PS_MATH_IX_C12_E05_020_Q01.png" width="80%"gt

Options

A. rhombus
B. trapezium
C. square
D. rectangle

Answer

D

Explanation

Since B is the mid-point of `bar(SR)` and PS=BR,PS=PA=AB.
`therefore` PABS is a rhombus, and similarly, AQRB is a rhombus.
`therefore angleBCA = angleADB=90^(@)`.
As PB and QB are bisectors of `angleP` and `angleQ, anglePBQ=90^(@)`.
`therefore CADB` is a rectangle.