Chapter 5.7, Problem 17PSB

a.

To determine

To find: The name of a quadrilateral which is symmetrical across both the diagonals.

Answer to Problem 17PSB

If a quadrilateral is symmetrical across both the diagonals, it is a rhombus.

Explanation of Solution

Given Information:

The quadrilateral is symmetrical about both the diagonals

Rhombus has two reflection symmetry across the diagonals.

This means, both the sides of a diagonal look alike.

Thus we can say that the rhombus is symmetrical about both of its diagonals.

Hence, if a quadrilateral is symmetrical about both the diagonals, it is a rhombus.

b.

To determine

To find: The name of a quadrilateral which is symmetrical across exactly one diagonal.

Answer to Problem 17PSB

If a quadrilateral is symmetrical acrossexactly one diagonal, it is a kite.

Explanation of Solution

Given Information:

The quadrilateral is symmetrical across one diagonal;

Kite is a quadrilateral that has only one line of symmetry and that is one of its diagonals.

This means, one of the diagonal create a reflection in kite.

Thus we can say that the kite is symmetrical about one of its diagonals.

Hence, if a quadrilateral is symmetrical acrossone of the diagonals, it is a kite.

c.

To determine

To find: The name of a quadrilateral which has four axes of symmetry.

Answer to Problem 17PSB

A quadrilateral having 4 axes of symmetry is a square.

Explanation of Solution

Given Information:

Quadrilateral has four axes of symmetry

Square is a quadrilateral that has only four axes of symmetry.

Two along the diagonals and the other two along the lines parallel to its sides and passing through its centre.

Hence, a quadrilateral having 4 axes of symmetry is a square.