If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a
(a) rhombus
(b) rectangle
(c) square
(d) parallelogram

Solution:

We have to find the type of quadrilateral that satisfies the given condition.

(i) A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides.

A rhombus has all four sides equal just like a square. That is why it is also known as a tilted square. The diagonals bisect each other at right angles.

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

(iii) A square is a two-dimensional plane figure with four equal sides. All angles are equal.

There are only two diagonals of the square and they bisect each other at right angles.

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

Therefore, a rectangle satisfies the given condition.

✦ Try This: The sum of all exterior angles of a pentagon is (a) 180°, (b) 360°, (c) 540°, (d) 720°

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 22

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a (a) rhombus (b) rectangle (c) square (d) parallelogram

Summary:

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a rectangle.

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