Question

Diagonals necessarily bisect opposite angles in a

Options

• rectangle

• parallelogram

• isosceles trapezium

• square

Answer 1

From the given choices, only in a square the diagonals bisect the opposite angles.

Let us prove it.

Take the following square ABCD with diagonal AD.

In ΔABD and ΔCBD:

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

 BD = BD (Common)

AB = DC  (Opposite sides of a square are equal.)

Thus,

 ΔABD ≅ ΔCBD (By SSS Congruence Rule)

By Corresponding parts of congruent triangles property we have:

∠ABD = ∠CBD

∠ADB = ∠CDB

Therefore, in a square the diagonals bisect the opposite angles.

Hence the correct choice is (d).