If a diagonal of a quadrilateral bisects both the angles, then it is a
(a) kite
(b) parallelogram
(c) rhombus
(d) rectangle

Solution:

Given, the diagonal of a quadrilateral bisects both the angles.

We have to find the type of quadrilateral.

(i) A Kite is a quadrilateral in which four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

(ii) A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

(iii) In a rhombus, opposite sides are parallel and the opposite angles are equal.

All the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles.

(iv) A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other.

Therefore, the diagonals bisect each other in a rhombus.

✦ Try This: If a diagonal of a quadrilateral do not bisect both the angles, then it is a (a) kite, (b) trapezoid, (c) rhombus, (d) rectangle

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 50

If a diagonal of a quadrilateral bisects both the angles, then it is a (a) kite (b) parallelogram (c) rhombus (d) rectangle

Summary:

If a diagonal of a quadrilateral bisects both the angles, then it is a rhombus.

☛ Related Questions:

• To construct a unique parallelogram, the minimum number of measurements required is (a) 2 (b) 3 (c) . . . .
• To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (c) 2 (d . . . .
• In quadrilateral HOPE, the pairs of opposite sides are __________. Fill in the blanks to make the st . . . .