Chapter 5.7, Problem 13PSB

a.

To determine

To find: The name for a quadrilateral whose opposite sides are parallel.

Answer to Problem 13PSB

It is a trapezium.

Explanation of Solution

Given Information:

Opposite sides of a quadrilateral are parallel

In the given quadrilateral, one pair of opposite sides are parallel.

We know that a quadrilateral whose one pair of opposite sides are parallel is a trapezium.

Hence, the given quadrilateral is a trapezium.

b.

To determine

To name: The given quadrilateral based on the data.

Answer to Problem 13PSB

It is a quadrilateral

Explanation of Solution

Given Information:

Measure of two opposite sides of a quadrilateral are 8 and 10

In the given quadrilateral, measures of the opposite sides are 8 and 10.

Here, it is a polygon with four sides and no relation between the sides is given.

Hence, it is a quadrilateral.

c.

To determine

To find: The name of a quadrilateral whose one pair of opposite sides are parallel and the other pair of opposite sides are equal.

Answer to Problem 13PSB

It is an isosceles trapezium.

Explanation of Solution

Given Information:

One pair of opposite sides are parallel

One pair of opposite sides are equal

In the given quadrilateral, one pair of opposite sides are parallel and the other pair of opposite sides are equal.

We know that a quadrilateral whose one pair of opposite sides are parallel is a trapezium.

Also, if the other pair of opposite sides are equal, then it becomes isosceles.

Hence, the given quadrilateral is an isosceles trapezium.

d.

To determine

To find: The name of a quadrilateral whose one pair of opposite sides are parallel and the other pair of opposite sides are equal.

Answer to Problem 13PSB

This quadrilateral is a rectangle.

Explanation of Solution

Given Information:

One pair of opposite sides are parallel

One pair of opposite sides are equal

In the given quadrilateral, all the angles are equal.

As the sum of all interior angles of a quadrilateral is ${360}^{\text{o}},$ so measure of each angle is ${90}^{\text{o}}.$

We know that a quadrilateral whose every angle is a right angle, is a rectangle.

Hence, the given quadrilateral is a rectangle.

e.

To determine

To find: The name of a quadrilateral whose diagonals are equal and bisect each other.

Answer to Problem 13PSB

This quadrilateral is a parallelogram.

Explanation of Solution

Given Information:

Diagonals are equal

Diagonals bisect each other

In the given quadrilateral, diagonals are equal and also they bisect each other.

We know that a quadrilateral whose diagonals are equal and bisect each other is a parallelogram.

Hence, the given quadrilateral is a parallelogram.

f.

To determine

To find: The name of a quadrilateral whose diagonals bisect each other at right angles.

Answer to Problem 13PSB

This quadrilateral is a rhombus.

Explanation of Solution

Given Information:

Diagonals bisect each other at right angles

In the given quadrilateral, diagonals bisect each other at right angles.

We know that a quadrilateral whose diagonals bisect each other at right angles is a rhombus.

Hence, the given quadrilateral is a rhombus.

g.

To determine

To find: The name of a quadrilateral whose one diagonal bisects the other at right angle.

Answer to Problem 13PSB

This quadrilateral is a kite.

Explanation of Solution

Given Information:

One of the diagonals bisect the other at right angle

In the given quadrilateral, one diagonal bisect the other at right angle.

We know that a quadrilateral whose one of the diagonals bisect the other at right angle is a kite.

Hence, the given quadrilateral is a kite.

h.

To determine

To find: The name of a quadrilateral whose one diagonal bisects the other.

Answer to Problem 13PSB

It is a quadrilateral.

Explanation of Solution

Given Information:

One of the diagonals bisect the other

In the given quadrilateral, one diagonal bisect the other.

From this data, we can’t conclude the type of quadrilateral.

Hence, it is a quadrilateral.