Even More Constructions

Constructing a Football Pitch

Constructing Parallel and Perpendicular Lines

Constructing a Square

Perpendicular Line Construction; through a Point NOT on the Line Draw a horizontal line and a point above that line. Label the line l and the point A.

• Take the compass and put the pointer on A. Open the compass so that it reaches beyond line l. Draw an arc that intersects the line twice.
• Move the pointer to one of the arc intersections. Widen the compass a little and draw an arc below the line. Repeat this on the other side so that the two arc marks intersect.
• Take your straightedge and draw a line from point A to the arc intersections below the line. This line is perpendicular to l and passes through A.

Theorem #1: If two lines are parallel and a third line is perpendicular to one of the parallel lines, it is also perpendicular to the other parallel line. Or, if l || m and l⊥n, then n⊥m.

Theorem #2: If two lines are perpendicular to the same line, they are parallel to each other.

Distance Between Parallel Lines The shortest distance between two parallel lines is the length of the perpendicular segment between them. It doesn’t matter which perpendicular line you choose, as long as the two points are on the lines. Recall that there are infinitely many perpendicular lines between two parallel lines.