Chapter 5.5, Problem 13PSA

a.

To determine

To find: The lines of symmetry of a rectangle.

Answer to Problem 13PSA

The lines of symmetry of the rectangle are $l\text{and}m.$

Explanation of Solution

Given Information:

The figure is a rectangle

Two dotted lines are $l\text{and}m$

In the rectangle, $l\text{and}m$ are the dotted lines

Now, if we take the line $l,$ so the parts above or below the line are congruent.

This means each side of a rectangle is a reflection of the other if we take the line $l.$

Thus, $l$ is the line of symmetry.

Similarly, if we take the line $m,$ each side of a rectangle is a reflection of the other.

Thus, $m$ is also the line of symmetry of the rectangle.

Hence, $l\text{and}m$ are the lines of symmetry.

b.

To determine

To find: The lines of symmetry of a kite.

Answer to Problem 13PSA

The line of symmetry of the kite is the line $p.$

Explanation of Solution

Given Information:

The figure is a kite

Two dotted lines are $n\text{and}p$

In the kite, $n\text{and}p$ are the dotted lines

Now, if we take the line $p,$ so the parts above or below the line are congruent triangles.

This means each side of a kite is a reflection of the other if we take the line $p.$

Thus, $p$ is the line of symmetry.

Now if we take the line $n,$ we get two triangles on either side of the line. But, the triangles are not congruent.

Thus, $n$ is not the line of symmetry.

Hence, $p$ is the line of symmetry.

c.

To determine

To find: The lines of symmetry of a rhombus.

Answer to Problem 13PSA

The lines of symmetry of the rhombus are the lines $q\text{and}r.$

Explanation of Solution

Given Information:

The figure is a rhombus

Two dotted lines are $q\text{and}r$

In the rhombus, $q\text{and}r$ are the dotted lines

Now, if we take the line $q,$ so the parts on either side of the line are two congruent triangles.

This means each side of a rhombus is a reflection of the other if we take the line $q.$

Thus, $q$ is the line of symmetry.

Similarly, if we take the line $r,$ each side of a rhombus is a reflection of the other.

Thus, $r$ is also the line of symmetry of the rhombus.

Hence, $q\text{and}r$ are the lines of symmetry.