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a.
To find: The name for a quadrilateral whose opposite sides are parallel.
a.
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 name: The given quadrilateral based on the data.
b.
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
Hence, it is a quadrilateral.
c.
To find: The name of a quadrilateral whose one pair of opposite sides are parallel and the other pair of opposite sides are equal.
c.
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 find: The name of a quadrilateral whose one pair of opposite sides are parallel and the other pair of opposite sides are equal.
d.
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
As the sum of all interior angles of a quadrilateral is
We know that a quadrilateral whose every angle is a right angle, is a rectangle.
Hence, the given quadrilateral is a rectangle.
e.
To find: The name of a quadrilateral whose diagonals are equal and bisect each other.
e.
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 find: The name of a quadrilateral whose diagonals bisect each other at right angles.
f.
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 find: The name of a quadrilateral whose one diagonal bisects the other at right angle.
g.
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 find: The name of a quadrilateral whose one diagonal bisects the other.
h.
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.
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