Line pairs

In the last lesson, you compared angles with the corner of a square. A set square has a corner that is a right angle too. Today, we will learn to spot perpendicular lines and parallel lines. Harpreet draws two train tracks, J K and L M, and a road, P Q, on a square grid. Is P Q parallel or perpendicular to J K? Is L M parallel or perpendicular to J K? Look at J K and P Q first. They cross at one point. Put the corner of a set square where they cross, with one edge along J K. P Q lies exactly along the other edge. So J K and P Q meet at a right angle. Lines that meet at a right angle are perpendicular lines. We mark the right angle with a small square. So P Q is perpendicular to J K. Now look at J K and L M. Count straight up from J to L: 1, 2, 3 squares. From M, count straight down to J K: 1, 2, 3 squares. So the gap between J K and L M stays the same. Lines that stay the same distance apart never meet. They are parallel lines, so we mark them with matching arrowheads. So L M is parallel to J K. Parallel lines can slope, like these two tracks.

On a map, road R S crosses road T U. Are R S and T U perpendicular? Write Yes or No. Try it first. Pause if you like. Put the corner of a set square where they cross, with one edge along R S. T U does not lie along the other edge. So R S and T U do not meet at a right angle. No, R S and T U are not perpendicular. Crossing lines are perpendicular only when they meet at a right angle.

On a map drawn on a square grid, G H is a train track. C D and E F are roads. Which road is parallel to G H? Try it first. Pause if you like. Count straight up from G to E: 1, 2, 3, 4 squares. From H, count straight up to F: just 1 square. So the gap between G H and E F changes. Now count straight down from G to C: 1, 2, 3 squares. From H, count straight down to D: 1, 2, 3 squares. So the gap between G H and C D stays the same. We mark G H and C D with matching arrowheads. So C D is parallel to G H. The flat road is not parallel to the track. Perpendicular lines meet at a right angle. Parallel lines stay the same distance apart, so they never meet.