1Find out what kind of pair each of these is: (a) the line segments EF and MN have the same slope and never meet, (b) the lines AB and CD cut at one point but the angle formed is not \( 90^\circ \), (c) the lines AB and XY cut at the point O and the angle formed is \( 90^\circ \), (d) the lines KL and RS cut each other at the point O.
2ABCD is a rectangle with A at the top left, B at the top right, C at the bottom left and D at the bottom right. (a) What kind of line segments are AB and CD? Why? (b) What kind of line segments are AC and CD? Why?
3Separate out the intersected lines, perpendicular lines and parallel lines in the capital letters E, H, N, T, X and L.
4Using a ruler, draw the line segments \( AB = 5 \) cm, \( XY = 8 \) cm, \( CD = 10 \) cm and \( MN = 7 \) cm, and use a set square to draw one line parallel to each of them.
5Using a ruler, draw the line segments \( PQ = 7 \) cm, \( ST = 12 \) cm, \( CD = 8 \) cm and \( GH = 9 \) cm, and use a set square to draw one line segment perpendicular to each of them.
6Draw a line segment \( PQ = 7 \) cm with a ruler and draw its perpendicular bisector using a compass.
7Fill in the blanks: (a) In \( \angle ABC \), ...... is the vertex and ...... and ...... are the arms. (b) One right angle equals ...... degrees. (c) Two right angles together make a ...... angle. (d) An angle greater than a straight angle but less than \( 360^\circ \) is called a ...... . (e) At quarter to eleven, the angle made by the minute hand and the hour hand of a clock is a ...... angle.
8Sort these angles by kind: \( 60^\circ \), \( 90^\circ \), \( 105^\circ \), \( 50^\circ \), \( 30^\circ \), \( 220^\circ \), \( 150^\circ \), \( 180^\circ \), \( 45^\circ \), \( 89^\circ \), \( 170^\circ \), \( 95^\circ \), \( 250^\circ \), \( 260^\circ \), \( 36^\circ \), \( 110^\circ \), \( 22^\circ \), \( 90^\circ \).
9Find the value of \( x^\circ \): (a) \( \angle PIG \) is a right angle and the ray IJ divides it into \( 38^\circ \) and \( x^\circ \). (b) \( \angle RBC \) is a straight angle and the ray BJ divides it into \( 65^\circ \) and \( x^\circ \).
10Draw an angle of \( 100^\circ \) with a protractor and then draw its bisector using a compass.
11Draw an angle of \( 135^\circ \) using a set square and a ruler.
12What happens if a radius of 4 cm is used on the compass to draw the perpendicular bisector of the line segment \( AB = 8 \) cm? Why?
13An angle measures \( 145^\circ \). What is the measure of the reflex angle on its outer side? Show the working.
14Why is every pair of perpendicular lines also a pair of intersected lines, while not every intersected pair is perpendicular? Explain with an example.
15What size of angle can be made by bisecting an angle of \( 90^\circ \) twice? Show the working.