Bisector of an angle using compass Constructing angles of 60
Answers
Answer:
This page shows how to construct (draw) a 60 degree angle with compass and straightedge or ruler. This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. We use one of those angles to get the desired 60 degree result. See the proof below for more details.
Printable step-by-step instructions
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
Proof
This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. The image below is the final drawing above with the red items added.
Argument Reason
1 Line segments AB, PB, PA are congruent All drawn with the same compass width.
2 Triangle APB is an equilateral triangle Equilateral triangles are those with all three sides the same length.
3 Angle APB has a measure of 60° All three interior angles of an equilateral triangle have a measure of 60°. See Equilateral triangle definition
- Q.E.D
Try it yThis page shows how to construct (draw) a 60 degree angle with compass and straightedge or ruler. This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. We use one of those angles to get the desired 60 degree result. See the proof below for more details.
Printable step-by-step instructions
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
Proof
This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. The image below is the final drawing above with the red items added.
Argument Reason
1 Line segments AB, PB, PA are congruent All drawn with the same compass width.
2 Triangle APB is an equilateral triangle Equilateral triangles are those with all three sides the same length.
3 Angle APB has a measure of 60° All three interior angles of an equilateral triangle have a measure of 60°. See Equilateral triangle definition
- Q.E.D
Try it yourself
Click here for a printable worksheet containing two 60° 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.
Answer:
Bisector of an angle using compass Constructing angles of 60
Hope this helps
Step-by-step explanation:
1. Place compass point on the vertex of the angle (point B).
2. Stretch the compass to any length that will stay ON the angle.
3. Swing an arc so the pencil crosses both sides (rays) of the given angle. You should now have two intersection points with the sides (rays) of the angle.
4. Place the compass point on one of these new intersection points on the sides of the angle.
If needed, stretch the compass to a sufficient length to place your pencil well into the interior of the angle. Stay between the sides (rays) of the angle. Place an arc in this interior (it is not necessary to cross the sides of the angle).
5. Without changing the span on the compass, place the point of the compass on the other intersection point on the side of the angle and make a similar arc. The two small arcs in the interior of the angle should be intersecting.
6. Connect the vertex of the angle (point B) to this intersection of the two small arcs.
You now have two new angles of equal measure, with each being half of the original given angle.