ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoin

1.	ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoints of AB, AC, CD and BD respectively, show that PQRS is a rhombus.
Answer» In ∆ ABC, P and Q are mid points of AB and AC respectively. So, PQ \|\| BC, and PQ = 1/2 …(1) Similarly, in ∆ADC, …(2) Now, in ∆BCD, SR = 1/2 …(3) Similarly, in ∆ABD, PS = 1/2 = 1/2 …(4) Using (1), (2), (3), and (4). PQ = QR = SR = PS Since, all sides are equal Hence, PQRS is a rhombus.

ABCD is a quadrilateral in which AD = BC. If P, Q, R, S be the midpoints of AB, AC, CD and BD respectively, show that PQRS is a rhombus.

Answer»

In ∆ ABC, P and Q are mid points of AB and AC respectively.

So, PQ || BC, and PQ = 1/2 …(1)

Similarly, in ∆ADC, …(2)

Now, in ∆BCD, SR = 1/2 …(3)

Similarly, in ∆ABD, PS = 1/2 = 1/2 …(4)

Using (1), (2), (3), and (4).

PQ = QR = SR = PS

Since, all sides are equal

Hence, PQRS is a rhombus.