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. 

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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