Question

Name the quadrilaterals whose diagonals.
A) bisect each other
B) are perpendicular bisectors of each other
C) are equal

Answer 1

Hint: First we will use the definitions of quadrilateral and their types of shapes like squares, rectangles and rhombus. Then we will check the properties of each shape, their sides, diagonals and angles.

Complete step by step solution: We know that in geometry, a quadrilateral is a closed, two-dimensional shape that has four straight sides.

A) We also know that the quadrilaterals whose diagonals are bisectors of each other are rhombus and squares.

We also know that the square is a flat shape with four equal straight sides, four right angles, opposite sides are parallel and whose diagonals bisect each other.

Since we know that a rhombus is a flat shape with four equal straight sides, opposite sides are parallel whose diagonals bisect each other.

This implies that rhombus and square are two shapes of a quadrilateral having diagonal, which bisect each other.

B) We also know that the quadrilaterals whose diagonals are perpendicular bisectors of each other are rhombus and squares again.

We also know that the square is a flat shape with four equal straight sides, four right angles, opposite sides are parallel and whose diagonals bisect each other at right angles.

Since we know that a rhombus is a flat shape with four equal straight sides, opposite sides are parallel whose diagonals bisect each other at right angles.

This implies that rhombus and square are again the two shapes of a quadrilateral having four sides with equal length.


C) We also know that the quadrilaterals that have four right angles are rectangles and squares.

Since we know that a rectangle is a flat shape with four equal right angles, opposite sides are equal and parallel and whose diagonals are equal in length.

We also know that the square is a flat shape with four equal straight sides, four right angles, opposite sides are parallel and whose diagonals bisect each other at right angles.

This implies that rhombus and square are only two shapes of a quadrilateral having four sides with equal length.

Note: In solving these types of questions, you need to know that the types of shapes in quadrilaterals like squares, rectangles and rhombus. Then we will check the properties of each shape, their sides and angles. This is a simple problem, one should only need to know the definitions.