Question

If the diagonals of a parallelogram are equal then what types of figures will form? Draw a rough diagram and give reasons

Answer 1

Referring to the figure, given that ABCD is a parallelogram and AC = BD (equal diagonals). ABCD is also a rectangle.

To prove: ABCD is a rectangle.

Proof:
AB = CD (opposite side of parallelogram)
AC = BD (given equal diagonals)
BC is the common side. 
So ΔABC is congruent to ΔBCD (SSS)
∴ ∠ABC = ∠BCD and AB// DC (opposite side of parallelogram)
∠ABC + ∠BCD = 180° (interior angles, AB//CD)

∠ABC = ∠BCD = 90° 

Since ABCD is a paralleogram and two of its interior angles are 90°, 
ABCD is a rectangle.