Perpendicular and Parallel Lines

Steps

1. 1

   Find two sides that point the same way and would never meet.

2. 2

   Draw the same arrow on both sides, pointing the same way.

3. 3

   For a second pair, use double arrows so the pairs do not mix up.

Worked example

1. 1

   $AD\perp AB$ — There is a small square at A, so AD and AB meet at 90°. Meeting at 90° is what perpendicular means.

2. 2

   $AB\parallel DC$ — AB and DC carry the same arrows. Matching arrows mark a parallel pair, so they point the same way.

3. 3

   $AD\perp DC$ — AD makes 90° with AB. DC points the same way as AB, so AD makes the same 90° with DC.

Steps

1. 1

   Plain paper: put the corner of a set square (or the 90° mark of a protractor) on the line at P.

2. 2

   Line one edge up with the line, then rule along the other edge through P.

3. 3

   Draw a small square at P to show the right angle.

Worked example

1. 1

   $l:3\text{ right},1\text{ up}$ — Count the squares along l, from one grid corner it passes through to the next. This step pattern is the line's direction.

2. 2

   $1\text{ right},3\text{ up}$ — Swap the two numbers. This is half of the quarter turn.

3. 3

   $1\text{ right},3\text{ down}$ — Now change up to down. Swap plus one change of direction turns the line through 90°.

4. 4

   $\text{from }P:1\text{ right},3\text{ down}$ — Start at P, count the steps and mark a dot. Rule a line through P and the dot, and draw the small square.