A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a __________.
(a) rhombus
(b) parallelogram
(c) square
(d) rectangle
Solution:
We have to find the type of quadrilateral with the given properties.
(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 parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.
(iii) A square is a two-dimensional plane figure with four equal sides.
There are only two diagonals of the square and they 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, rhombus satisfies all the given properties.
✦ Try This: How many diagonals does a parallelogram have?
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 17
A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a __________. (a) rhombus (b) parallelogram (c) square (d) rectangle
Summary:
A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a rhombus.
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