Understanding and Mastering Perpendicular Lines and How to Draw Them

Perpendicular lines meet at 90 degrees, and on a graph their slopes are negative reciprocals. Parallel lines never meet and have equal slopes, which is the algebraic test for each.

Worked examples: drawing perpendicular lines

Practice questions on perpendicular lines

1. Draw a line (EF). Now, without using a protractor, can you draw a line (GH) perpendicular to (EF) using only a compass and straightedge? (Hint: Think about constructing equal arcs!)
2. Why is it essential for buildings and structures to have perpendicular walls? What could be the implications if they aren’t?
3. In the world around you, list five instances where perpendicular lines play a role.

1. Yes, with a compass and straightedge, one can draw perpendicular bisectors. Here’s how:

• Place the compass on a point on line (EF) and draw an arc above and below the line.

• Without changing the compass width, place it on another point on line (EF) and draw another set of arcs that intersect the first set.

• Draw a line through the two points where the arcs intersect. This line is perpendicular to (EF).

1. Perpendicular walls are essential for structural stability. Non-perpendicular walls can lead to uneven weight distribution, making the building prone to collapse. It also affects the aesthetics and functionality of interiors.
2. Examples: Corners of books, the intersection of roads, the edges of a chessboard, the frame of a door, and the structure of window panes.

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