Page 223 - Ganit Kaushal

5. Set-Squares: These are two triangular tools in the geometry box – one of
them has 45°, 45°, 90° angles at the vertices, and the other has 30°, 60°, 90° 45°
angles at the vertices. The two perpendicular sides of either set-squares are
graduated into centimetres. They are used to draw parallel and perpendicular 45°
lines. 30°
After knowing our geometric tools, now it’s time to learn how to use them
to construct a few well-known plane geometrical shapes. 60°

8.3 THE CIRCLE Set-squares

A circle is a closed curve in which every point on the boundary is at the same distance from a point inside it.
The point inside is called the centre of the circle, and the distance between the centre and any point on the
boundary is called the radius of the circle.
Now, let us learn how to construct a circle with the help of a compass and a ruler:

Construction of a Circle with a Given Radius

Construction 1: Draw a circle of radius 4 cm.
Sol. Follow the steps given below:

Step 1: Use a ruler to set the distance from the pointer of
the compass to the pencil’s lead at 4 cm.
Step 2: Mark a point which is the centre (say C) of the
circle with a sharp pencil.
Step 3: Place the pointer of the compass at the centre C
of the circle. Radius Centre
C
Step 4: Draw the circle by turning the compass slowly
through 360°.
After completing step 4, the full circle will look as given below.
Circumference
C is the centre of the circle. The boundary of the circle is also called its circumference.
Any line segment (say AB) that passes through the centre and has its ends on the B
circumference is called the diameter of the circle. Take any three points P, Q and D
on the circumference. Measure CP, CQ, and CD. Centre C Radius

What do you observe? Are they all equal? Diameter D
A
Right you are! Yes, they are all equal to 4 cm. They are all the radius of the
circle. Also, observe that Diameter = 2 × Radius. P Q

8.4 THE LINE SEGMENT

In geometry, a line segment is part of a line that is bounded by two distinct end points, A and B.

Construction 2: Draw a line segment of length 5 cm using a ruler and compass.
Sol. Follow the steps given below:
Step 1: Draw a line l of any length. Mark a point A on the line A l
l, which will be the starting point of the line segment.

Playing with Constructions 221