In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ see Fig. Show that:

(i) Δ APD ≅ Δ CQB

(ii) AP = CQ

(iii) Δ AQB ≅ Δ CPD

(iv) AQ = CP

(v) APCQ is a parallelogram

Diagonal AC of a parallelogram ABCD bisects ∠A. Show that

(i) it bisects ∠C also,

(ii) ABCD is a rhombus.

(Ex.8.1Q3.png)

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that :

(i) ABCD is a square

(ii) diagonal BD bisects ∠B as well as ∠D.

Show that the diagonals of a square are equal and bisect each other at right angles.