1.

In Fig. ABCD and PQRC are rectangles and Q is the mid-point of AC. Prove that(i) DP = PC (ii) PR =  \(\frac{1}{2}\)AC.

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 = \(\frac{1}{2}\) BD

PR = \(\frac{1}{2}\) AC

∵ diagonals of rectangle are equal

Proved.



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