Page 122 - Mathematics Coursebook

12.2 Drawing perpendicular and parallel lines

12.2 Drawing perpendicular and parallel lines

Perpendicular lines are lines that meet at a right angle (90°).
You show that lines are perpendicular by using a small square symbol in the
corner ( ). You have already seen this in Unit 5.
Parallel lines are lines that never meet.

!e perpendicular distance between the lines is always the same.
You show that lines are parallel by using an arrow symbol (→) on each line.
You can use a ruler and set square to draw parallel and perpendicular lines.

A B
Worked example 12.2 5 6 7 8
4
cm
3
2
1
a Draw a line segment AB 7.5 cm long. Mark the point C on the line AB where C is 4.5 cm from A.
B
Draw a line from C that is perpendicular to the line AB.
A
C
b Draw parallel lines 5 cm long that are a distance of 2 cm apart.
8
1
4
5
6
2
7
3
cm
a
First draw AB, 7.5 cm long.
Mark the point C on the line AB, so that AC is 4.5 cm.
Use the set square to draw a perpendicular line up
A B
A C B from C.
cm cm 1 1 2 2 3 4 3 5 4 6 5 7 8
b First draw one line segment 5 cm long.
Place the set square at the end of this line and use it
to measure 2 cm up from the fi rst line.
Use the set square to measure another point 2 cm up
from the fi rst line.
Join these two points and make sure that the parallel
line is also 5 cm long.

) Exercise 12.2

1 Draw parallel line segments that are:
a 7 cm long and 1.5 cm apart b 9.8 cm long and 3.2 cm apart
2 Draw PQ 10 cm long. Mark the point R on PQ so that R is 3 cm from P.
Mark the point S on the line PQ so that S is 4.5 cm from Q.
Draw two lines, one from R and one from S, that are both perpendicular to the line PQ.
3 Draw UV 8 cm long.
a Draw a 4 cm line perpendicular to UV from the midpoint of UV. Label the ends X and Y.
b Draw a line, 4 cm long, from the midpoint of XY and perpendicular to XY. Label the ends W and Z.
c Check by measuring with a ruler that WZ is parallel to UV.

12 Constructions 121