Constructing a 45 degree angle with compass and straightedge or ruler

Constructing a 45° angle Using compass and straightedge or ruler

- Printable problem worksheet
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Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping. (If there is no image below, see support page.)

Step-by-step Instructions

After doing this	Your work should look like this
1. Draw a line segment which will become one side of the angle. (Skip this step if you are given this line.) The exact length is not important. Label it PQ. P will be the angle's vertex.
In the next 3 steps we create the perpendicular bisector of PQ. See Constructing a perpendicular bisector of a line segment
2. Set the compass width to just over half the length of the line segment PQ.
3. With the compass point on P then Q, draw two arcs that cross above and below the line.
4. Draw a line between the two arc intersections. This is at right angles to PQ and bisects it (divides it in exactly half).

5. With the compass point on the intersection of PQ and the perpendicular just drawn, set the compass width to P
6. Draw an arc across the perpendicular, creating the point C
7. Draw a line from P through C, and on a little more. The end of this line is point R
8. Done. The angle ∠QPR has a measure of 45°

Try it yourself

Click here for a printable worksheet containing two 45° angle exercises. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

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