2nd Class Mathematics Geometrical Figures Geometrical Figures

Geometrical Figures

 

Line

Let's see the lines given below:

           

 

•           Example:

Give the name of all slant lines from the figure given below.

(a) AD and BC                                                   (b) AB and BC

(c) AB and AD                                                   (d) All the above

(e) None of these

Ans.     (a)

 

•           Example:

Which one of the following is correct about the line?

(a) A straight line is measured by ruler.

(b) A straight line cannot be measured by ruler

(c) A straight line is measured in grams,

(d) All the above

(e) None of these

Ans.     (a)

Note: We use ruler to measure a straight line.

 

Angle

An angle is formed at the meeting point of two lines or an angle is formed when two lines meet. The point where two lines meet is called vertex. See the figures given below:

 

•           Example:

Which one of the following is correct about the angle?

(a) Both sides of an angle must be equal in length

(b) Both sides of an angle may be unequal in length

(c) Two lines cannot form an angle

(d) Three lines are required for formation of an angle

(e) None of these

Ans.     (b)

 

•           Example:

Which one of the following is representing an angle?

 

Ans.     (c)

Note: Both the sides of an angle may be unequal in length.

Square

A square has four equal sides and tour equal angle.

In this picture side AB = BD = CD = AC

And \[\angle \]A = \[\angle \]B = \[\angle \]C = \[\angle \]D = \[90{}^\circ \]

 

•           Example:

If the sum of three angles of a square is \[\mathbf{270}{}^\circ \], then the measurement of its fourth angle will be?

(a) \[70{}^\circ \]                                                    (b) \[80{}^\circ \]

(c) \[90{}^\circ \]                                                    (d) All the above

(e) None of these

Ans.     (c)

Explanation: Each angle of the square is \[90{}^\circ \]

 

•          Example:

What will be the sum of length of two sides of a square, if the sum of length of its other two sides is 20 cm?

(a) 20 cm                                                           (b) 40 cm

(c) 10 cm                                                           (d) All the above

(e) None of these

Ans.     (a)

Explanation: All the sides of square are equal.

 

Quadrilateral

Properties

A quadrilateral has:

1. 4 sides (edges)

2. 4 vertices (corner)

 

The following are the quadrilaterals:

 

•           Example:

A plane figure has four sides and four vertices. The name of the plane figure is

(a) Quadrilateral                                                 (b) Triangle

(c) Pentagon                                                    (d) All the above

(e) None of these

Ans.     (a)

 

Rectangle

Properties

In a rectangle:

1. Opposite sides are equal.         

2. Opposite sides are parallel.

3. All angles are equal.

See the figure given below:

Here,

AB = CD

And AC = BD

\[\angle \]A = \[\angle \]B = \[\angle \]C = \[\angle \]D = \[90{}^\circ \]

Similarly

is also a rectangle.

 

•           Example:

Which one of the following is correct about a rectangle, if a pair of opposite sides is PQ and RS, another pair of opposite sides is PS and QR?

(a) PQ \[\ne \] RS and PS = QR                           (b) PQ = RS and PS = QR

(c) PQ = PS = RS = QR                                 (d) All of these

(e) None of these

Ans.     (b)

Explanation: Opposite sides of a rectangle are equal

Note: A rectangle is a quadrilateral.

 

Rhombus

Properties

In a rhombus:

1. All sides of a Rhombus are equal.

2. Diagonals of a rhombus are perpendicular to each other. That is they intersect at\[90{}^\circ \].

 

See the figure given below:

Here, the sides

AB = BC = CD = AD

See 1 more Rhombus.

Note: Rhombus is also a quadrilateral. Each angle of a rhombus may not be right angle.

 

•           Example:

Which one of the following differentiates the rhombus and square?

(a) Rhombus has all equal sides

(b) Rhombus has all unequal sides

(c) Each angle of a rhombus may not be a right angle

(d) All the above

(e) None of these

Ans.     (c)

 

Parallelogram

Properties

In a parallelogram:

1. Opposite sides are equal

2. Opposite angles are equal.

See the parallelogram given below:

Here, the sides AB = CD & AB | | CD

AD = BC & AD | | BC.

And the opposite angles, \[\angle \]A = \[\angle \]C & \[\angle \]B = \[\angle \]D

 

Let's see another parallelogram given below:

 

•           Example:

Measurement of an angle of a parallelogram is 40. What will the measurement of its opposite angle?            

(a) \[40{}^\circ \]                                                          (b) \[140{}^\circ \]

(c) \[150{}^\circ \]                                                         (d) All the above

(e) None of these

Ans.     (a)

Explanation: Opposite angles of a parallelogram are equal

Note: Parallelogram is also a quadrilateral

 

Trapezium

In a trapezium, a pair of opposite sides is parallel

This is a trapezium in which a pair of opposite sides is parallel.

See the figure given below:

In the trapezium given above AB and CD are parallel.

 

•           Example:

Two opposite sides of a room are parallel and its other two opposite sides are not parallel. Which one of the following is the shape of the room?

(a) Trapezium                                                     (b) Parallelogram

(c) Hexagon                                                       (d) All the above

(e) None of these

Ans.     (a)

Explanation: One pair of opposite sides are parallel in trapezium.

Note: Trapezium is also a quadrilateral