Question

The two diagonals are equal in a

Options

• parallelogram

•  rhombus

•  rectangle

• trapezium

Answer 1

Two diagonals are equal only in a rectangle.

This can be proved as follows:

The rectangle is given as ABCD, with the two diagonals as AD and BC.

In ΔADB and ΔBCD:

 AD = BC (Opposite sides of a rectangle are equal.)

CD = CD (Common)

∠ADC = ∠BCD  (Each angle in a rectangle is a right angle)

Thus,

ΔADB ≅ ΔBCD  (By SAS Congruence Rule)

By Corresponding parts of congruent triangles property we have:

AC = BD

Therefore, in a rectangle the two diagonals are equal.

Hence the correct choice is (c).