###
**Construction of Lines **

Steps to construct a line segment of length 5 cm:

1.Draw line l.

2.Mark a point on line and name it P.

4.Place the pointer of the compass on point P.

6.PQ is the required line segment of length 5 cm.

**Two lines are said to be perpendicular when they intersect each other at an angle of 90o.**

The perpendicular bisector is a perpendicular line that bisects another line into two equal parts.

### Constructing of Angles

###
An exact copy of a line segment can be constructed using a ruler and a compass.

**To construct a copy of an angle:**

- Draw a line AB.
- Mark any point O on AB.
- Place the compass pointer at vertex X of the given figure and draw an arc with a convenient radius, cutting rays XY and XZ at points E and F, respectively.
- Without changing the compass settings, draw an arc on line AB from point O. It cuts line AB at P.
- Set the compass to length EF.
- Without changing the compass settings, draw an arc from P cutting the previous arc at point Q.
- Join points O and Q.
- Hence, ∠POQ is the required copy of ∠YXZ.

**To construct the bisector of an angle:**

Let the given angle be LMN.

Place the compass pointer at vertex M of the given angle.

Draw an arc cutting rays ML and MN at U and V, respectively

Draw an arc with V as the centre and a radius more than half the length of UV in the interior of ∠LMN.

Draw another arc with U as the centre and the same radius intersecting the previous arc.

Name the point of intersection of the arcs as X.

Join points M and X.

Thus, the ray MX is the required bisector of ∠LMN

**Steps to construct a 60° angle:**

- Draw a line.
- Mark point P on the line.
- Draw an arc from point P with a convenient radius cutting the line at a point.
- Name the point of intersection of the arc and the line as Q.
- Draw another arc with Q as the centre and the same radius so that it passes through point P.
- Name the point of intersection of the two arcs as R.
- Join points P and R.

**In a similar way, we can construct:**

A 900 angle without using the protractor

A 1200 angle without using the protractor

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