Education Standards
How to construct a 60 degree angle
Constructing Angles
Overview
How to construct different angles using a straight edge and a compass.
60 degree angle
| 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. | |
| 2. Set the compasses on P, and set its width to any convenient setting. | |
| 3. Draw an arc across PQ and up over above the point P. | |
| 4. Without changing the compasses' width, move the compasses to the point where the arc crosses PQ, and make an arc that crosses the first one. | |
| 5. Draw a line from P, through the intersection of the two arcs. | |
| 6. Done. The angle QPR has a measure of 60° |
Construct a 60° angle, with compass and straightedge
(For assistance see www.mathopenref.com/constangle60.html)
| 1. | Construct a 60° angle with its vertex at the point P |
| 2. | Perform the construction twice to create a 120° angle from two 60° angles that are adjacent (share a side) as in the example: |
(C) Copyright John Page 2017
45 degree angle
| 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 compasses' width to just over half the length of the line segment PQ. | |
| 3. With the compasses' 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 compasses' point on the intersection of PQ and the perpendicular just drawn, set the compasses' 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° |
Construct a 45° angle, with compass and straightedge
(For assistance see www.mathopenref.com/constangle45.html)
| 1. | Construct a 45° angle with its vertex at the point P |
| 2. | (a) | Construct a 45° angle on each end of the line below as in the example. | Example |
| (b) | What is the precise name of the triangle that results? | ||
| (c) | What properties does this triangle have? (list 3). |
(C) Copyright John Page 2017