Discover Mathematics P4: Term 2, Unit 12, Lessons 1–5
GoalTell parallel, intersecting and perpendicular lines apart and find them in shapes.
New words
parallel lines · lines in the same flat surface that never meet and stay the same distance apartintersecting lines · lines that cross at one pointperpendicular lines · intersecting lines that make a right angle (a square corner)
Explanation
Two lines on a flat surface can be related in three ways. Parallel lines never meet, however far we draw them, and they stay the same distance apart, like the two rails of a train track. Intersecting lines cross each other at one point. Perpendicular lines are special intersecting lines: they cross to make a right angle, which is a square corner like the corner of a page. So all perpendicular lines are intersecting, but not all intersecting lines are perpendicular. In a rectangle, opposite sides are parallel and neighbouring sides are perpendicular. In the picture we use small arrow marks for parallel sides and a small square for a right angle.
Worked examples
Parallel lines. The two lines in the picture are the same distance apart all along, and the arrow marks show they are parallel. A ladder’s two long sides and the lines on a notebook page are parallel.
Intersecting lines. These two lines cross at the point O. They meet at one point only. They do not make a square corner, so they are intersecting but not perpendicular.
Perpendicular lines. These lines cross at O and make a right angle, shown by the small square. The two edges of a door frame at a corner are perpendicular. A plus sign + is made of two perpendicular segments.
Class activity
Lines in the room. Find parallel lines, intersecting lines and perpendicular lines in your room: edges of the table, the window, the door and the floor tiles. Write three examples of each kind. Use the corner of a sheet of paper to test whether two lines are perpendicular.
Practice
1
Look at lines AB and CD. Are they parallel, intersecting or perpendicular? Explain.
They intersect, but they do not make a square corner, so they are not perpendicular.
2
Give two examples of parallel lines in your classroom.
For example: the top and bottom edges of the board; two rows of lines in a notebook.
3
How many pairs of parallel sides does a rectangle have?
Two pairs: the two long sides and the two short sides.
4
What kind of lines form the corner of your notebook?
Perpendicular lines, because they make a right angle.
5
Hana draws two lines that do not touch on her page, but they get closer and closer. Are they parallel?
No. Parallel lines stay the same distance apart. If we extend these lines they will meet, so they are intersecting.
