In Fig. 14.100, ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that

Question

In Fig. 14.100, ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that (i) DP = PC (ii) PR = AC.

Philoid · Accepted Answer

(i) In ∆ADC , Q is mid point of AC such that

PQ││AD

∴ P is mid point of DC

= DP= DC (converse of mid point theorem)

(ii) Similarly, R is the mid point of BC

= PR=

PR= ∵ diagonals of rectangle are equal

Proved.