22 August 2014

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.

3.Open the compass to measure the length of the line segment                                  by placing the pointer on the 0 mark of the ruler and the pencil                                 point on the 5 cm mark.

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

5.Swing an arc on the line to cut it at Q.

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.

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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