In case of a parallelogram prove that :

(i) the bisectors of any two adjacent angles intersect at 90°.

(ii) the bisectors of opposite angles are parallel to each other.

The diagonals of a rectangle intersect each other at right angles. Prove that the rectangle is a square.

In the following figure, ABCD is a rhombus and DCFE is a square.

If ∠ABC = 56°, find :

(i) ∠DAE

(ii) ∠FEA

(iii) ∠EAC

(iv) ∠AEC

In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that :

(i) AE = AD

(ii) DE bisects angle ADC

(iii) angle DEC is a right angle