#### Solved Examples and Worksheet for Two-dimensional Geometric Figures

Q1Which one of the figures shown represents a trapezoid? A. Figure A
B. Figure B
C. Figure C
D. Figure D

Step: 1
A trapezoid is a quadrilateral that has exactly one pair of parallel sides.
Step: 2
From the figures, figure C is a quadrilateral and has exactly one pair of parallel sides.
Step: 3
Figure C represents a trapezoid.
Correct Answer is :   Figure C
Q2A triangle in which all sides and all angles are equal is called ______ triangle.

A. an equilateral
B. a scalene
C. an isosceles
D. a right

Step: 1
A triangle in which all the three sides are equal and all angles are equal is called an equilateral triangle.
Correct Answer is :   an equilateral
Q3Identify a parallelogram. A. Figure 1
B. Figure 2
C. Figure 3
D. All the above

Step: 1
A parallelogram is a quadrilateral in which, the pair of opposite sides are parallel and opposite angles are equal.
Step: 2
All the figures given in the choices A, B, and C are parallelograms.
[The opposite sides and angles are equal in all figures.]
Correct Answer is :   All the above
Q4How many vertices are there in the figure? A. 2
B. 6
C. 4
D. 5

Step: 1
The common end point of the two rays or line segments forming an angle is called the vertex.
Step: 2
A,B,C and D are the vertices.
Step: 3
So, there are 4 vertices.
Q5The measure of one of the three angles in a triangle is 90°. Name the triangle.
A. right triangle
B. scalene
C. isosceles
D. equilateral

Step: 1
A triangle in which one angle measures 90° is a right triangle.
Correct Answer is :   right triangle
Q6Which of the statements is true?
A. An equilateral triangle has three angles equal.
B. One angle in an equilateral triangle is equal to 90°.
C. An equilateral triangle has none of angles equal.
D. An equilateral triangle has only two angles equal.

Step: 1
An equilateral triangle is a triangle in which all the three sides and the angles are congruent.
Step: 2
So, the statement, 'An equilateral triangle has three angles equal', is true.
Correct Answer is :   An equilateral triangle has three angles equal.
Q7Which of the figures is a hexagon? A. Figure 1
B. Figure 2
C. Figure 3
D. Figure 4

Step: 1
A hexagon is a closed figure formed by joining six line segments.
Step: 2
Among the figures, Figure 2 has 6 sides.
Step: 3
So, Figure 2 is a hexagon.
Correct Answer is :   Figure 2
Q8Which of the figures is an octagon? A. Figure 3
B. Figure 4
C. Figure 1
D. Figure 2

Step: 1
An octagon is ' eight sided polygon ' .
Step: 2
So, Figure 3 is an octagon.
Correct Answer is :   Figure 3
Q9Which quadrilateral has four congruent sides?

A. square or rectangle
B. trapezoid
C. rectangle or isosceles trapezoid
D. rhombus or square

Step: 1
[Given.] Step: 2
A quadrilateral with four congruent sides is a rhombus or a square.
[By definition.]
Correct Answer is :   rhombus or square
Q10The teacher told Greg to draw a polygon with more than 4 sides. Which one of the following can he draw?
A. triangle
B. square
C. rectangle
D. pentagon

Step: 1
Among the choices given, a triangle has 3 sides, a square and a rectangle have 4 sides each, and a pentagon has 5 sides.
Step: 2
5 > 4 > 3
Step: 3
So, Greg can draw a pentagon.
Q11Which of the following describes a parallelogram?
A. 4 right angles
B. 2 right angles
C. 2 pairs of parallel lines
D. 4 equal sides

Step: 1
A quadrilateral with two pairs of opposite sides parallel is called a parallelogram.
Step: 2
So, among the choices, 2 pairs of parallel lines best describes the parallelogram.
Correct Answer is :   2 pairs of parallel lines
Q12Which quadrilateral has 4 sides equal? A. Figure 2
B. Figure 3
C. Figure 1
D. Figure 4

Step: 1
Step: 2
From the given figures, Figure 3 is a square. So, Figure 3 has 4 sides of equal length.
Correct Answer is :   Figure 3
Q13Name the shape that is between the circle and the square. A. rectangle
B. circle
C. triangle
D. square

Step: 1
The shape between the circle and square is a rectangle because it has 4 right angles and opposite sides are equal.
Q14Which 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
Q15Classify the triangle whose sides measure 7 in., 7 in., and 7 in.
A. scalene triangle
B. isosceles trianlge
C. equilateral triangle

Step: 1
The lengths of the three sides of a triangle are same, and equal to 7 in.
Step: 2
So, the triangle is an equilateral triangle.
Correct Answer is :   equilateral triangle