#### Solved Examples and Worksheet for Attributes of Quadrilaterals

Q1I am the door to your room. I have my one pair of sides longer than the other. What shape am I?

A. square
B. rectangle
C. circle
D. pyramid

Step: 1
A rectangle is a quadrilateral with two pairs of parallel sides, two pairs of equal sides, and four angles measuring 90° each.
Step: 2
A door has two pairs of parallel sides and two pairs of equal sides.
Step: 3
So, I am rectangular in shape.
Q2Which of these shapes have four sides? A. rectangle
B. circle
C. I don′t know.
D. triangle

Step: 1
A rectangle has four sides.
Step: 2
Therefore, the correct answer is rectangle.
Q3Which one of the following figures is a quadrilateral? A. Figure 4
B. Figure 3
C. Figure 2
D. Figure 1

Step: 1
Step: 2
Figures 1, 3 and 4 do not have 4 sides.
Step: 3
So, Figure 2 is a quadrilateral.
Correct Answer is :   Figure 2
Q4Which quadrilateral has its opposite sides equal? A. Figure 4
B. Figure 3
C. Figure 1
D. Figure 2

Step: 1
A quadrilateral with opposite sides equal is called a parallelogram.
Step: 2
From the given figures, Figure 1 is a parallelogram with opposite sides equal.
Step: 3
So, Figure 1 is the correct answer.
Correct Answer is :   Figure 1
Q5Which of the following names appear to describe the quadrilateral MNOP? A. square
B. rectangle
C. parallelogram
D. trapezoid

Step: 1
In the given quadrilateral MNOP opposite sides are parallel, equal and opposite angles are equal.
Step: 2
Therefore, the given quadrilateral MNOP is a parallelogram.
A. Six
B. Three
C. Five
D. Four

Step: 1
All four sided polygons are known as quadrilaterals.
Step: 2
So, any quadrilateral has four sides.
Q7Identify the figure that is a square. A. Figure 4
B. Figure 2
C. Figure 3
D. Figure 1

Step: 1
A square is a four sided polygon whose all sides are equal and all the angles measure 90°.
Step: 2
Figure 2, Figure 3 and Figure 4 have all their opposite sides equal.
Step: 3
Figure 1 is a square, as all its sides are equal.
Correct Answer is :   Figure 1
Q8Which one of the figures is a rectangle? A. Figure 1
B. Figure 2
C. Figure 3

Step: 1
A four-sided figure whose opposite sides are parallel and all the angles measure 90° is called a rectangle.
Step: 2
Among the choices, Figure 3 is a rectangle.
Correct Answer is :   Figure 3
Q9Which quadrilateral does not have the following properties?
'Opposite sides are parallel and of the same length.'

A. parallelogram
B. rectangle
C. square
D. kite

Step: 1
A rectangle, a square and a parallelogram have its opposite sides parallel and of the same length.
Step: 2
A kite has two pairs of sides of same length but opposite sides are not parallel.
Step: 3
Hence, kite is the quadrilateral which does not satisfy the properties 'opposite sides are parallel and of the same length.'
Q10Choose the quadrilateral or quadrilaterals in which the two pairs of opposite angles are equal. A. I and II
B. I and III
C. II and III
D. I, II, and III

Step: 1
Observe that, figure 'I' is a trapezoid, figure 'II' is a rhombus, and figure 'III' is a parallelogram.
Step: 2
In a trapezoid, both pairs of opposite angles are not equal.
[From properties of a trapezoid.]
Step: 3
In a parallelogram, both pairs of opposite angles are equal.
[From properties of a parallelogram.]
Step: 4
A rhombus is a parallelogram. So, the properties that are true for a parallelogram are true for a rhombus as well.
Step: 5
Therefore, the choice "II and III" is the correct answer.
Correct Answer is :   II and III
Q11Identify the quadrilaterals in which all the sides are equal. A. I and II
B. I and III
C. II and III
D. I, II, and III

Step: 1
All the sides of a rhombus are equal.
Step: 2
A square is a rhombus.
Step: 3
All the properties that are true for a rhombus are also true for a square. So all the sides of a square are also equal.
Correct Answer is :   II and III
Q12Recognize the rhombus in which every angle is a right angle.
A. Trapezoid
B. Square
C. Rectangle
D. Right Triangle

Step: 1
From the given options, a rhombus in which every angle is a right angle is a square.
Q13Which of the following statements is not true?

A. Every parallelogram is a trapezoid.
B. Every rectangle is a parallelogram.
C. Every Square is a rectangle.
D. Every trapezoid is a parallelogram.

Step: 1
Every Square is a rectangle because a square satisfies all the properties of rectangle.
Step: 2
Every rectangle is a parallelogram because in a rectangle, two pairs of opposite sides are parallel.
Step: 3
Every parallelogram is a trapezoid but every trapezoid is not a parallelogram. because, in a trepezoid one pair of opposite sides may not be parallel.
Correct Answer is :   Every trapezoid is a parallelogram.