


Congruent line segments: 

Definition 
Line segments having the same length.



 A line segment is denoted using capital letters at both ends.


Example 

We can see that both line segments, \(PQ\) and \(RS\), have the same length.
Thus, \(PQ\) and \(RS\) are congruent.



Congruent angles: 

Definition 
Angles having the same size.





Example 

We can see that,
\(\angle PQR=40^\circ\) or \(\angle RQP=40^\circ\).
Thus, \(\angle PQR\) and \(\angle RQP\) are congruent.



Estimate and measure the length of a line segment and the size of an angle: 

 An angle that appears more than a right angle has an angle greater than \(90^\circ\).
 An angle that appears less than a right angle has an angle less than \(90^\circ\).




 The size of an angle can be measured more accurately using a protractor.


The properties of the angle on a straight line, a reflex angle and the angle of one whole turn: 

The angle on a straight line
 The sum of angles on a straight line is \(180^{\circ}\).


Reflex angle


The angle of one whole turn


The properties of complementary angles, supplementary angles and conjugate angles: 

Complementary angles
 The sum of the two angles is always \(90^\circ\).


Supplementary angles


Conjugate angles


Perform a geometrical construction: 

(i) Line segments
 A section of a straight line with a fixed length.


Example 
Construct the line segment \(AB\) with a length of \(8\text{ cm}\) using only a pair of compasses and a ruler.




(ii) Perpendicular bisectors
 If line \(AB\) is perpendicular to line segment \(CD\) and divide \(CD\) into two parts of equal length, then line \(AB\) is known as the perpendicular bisector of \(CD\).


Example 
Construct the perpendicular bisector of line segment \(PQ\) using only a pair of compasses and a ruler.




(iii) Perpendicular line to straight line
 If a line is perpendicular to line \(PQ\), then the line is known as perpendicular line to line \(PQ\).


Example 
Using only a pair of compasses and a ruler, construct the perpendicular line from point \(M\) to the straight line \(PQ\).




(iv) Parallel lines
 Lines that will never meet even when they are extended.


Example 
Using only a pair of compasses and a ruler, construct the line that is parallel to \(PQ\) passing through point \(R\).




Construct angles and angle bisectors: 

(i) Constructing an angle of \(60^{\circ}\) 

Example 
Using only a pair of compasses and a ruler, construct line \(PQ\) so that \(\angle PQR=60^\circ\).




(ii) Angle Bisectors
 A line divides an angle into two equal angles.


Example 
Using only a pair of compasses and a ruler, construct the angle bisector of \(\angle PQR\).



