Hi I needed to construct a 60 degree angle with only a ruler and compasses. I understand how to construct an angle of 90 degrees, and how to do an angle bisector but cannot understand how to do this.
Thankyou
Hi I needed to construct a 60 degree angle with only a ruler and compasses. I understand how to construct an angle of 90 degrees, and how to do an angle bisector but cannot understand how to do this.
Thankyou
Hello,
In an equilateral triangle, angles are 60 degrees.
So you can try to do this way :
- let A and B be two points of the plane
- get the length AB with your compass
- draw the circle of center A, and length AB. This will make all the points that are at equal distance to A than B.
- draw the same circle, but of center B. This will make all the points that are at equal distance to B than A.
There will be two intersections. See what the properties of the sides of the formed triangle are
Hello, Turple!
We need to construct an equilateral triangle.I needed to construct a 60° angle with only a ruler and compass.
Draw a horizontal line; label the left end $\displaystyle A.$
Open your compass to a convenient spread (and don't change it).
Place the point on $\displaystyle A$ and swing an arc cutting the line at $\displaystyle B.$
Keep the point on $\displaystyle A$ and swing an arc above the line.
Place the point on $\displaystyle B$ and swing an arc cutting the first arc at $\displaystyle C.$
Triangle ABC is equilateral.
Therefore: .$\displaystyle \angle A \,=\,\angle B\,=\,\angle C \,=\,60^o$
Edit: Too fast for me, Moo!
.
1. Draw a circle around midpoint M
2. Draw a diameter. I labeled the endpoints of the diameter by A and B.
3. Construct a perpendicular bisector of MB which cuts the circle line in 2 points.
4. Connect one of the intersection points with M. I've labeled the point in question by C.
5. The angle $\displaystyle \angle(BMC)=60^\circ$
By the way: This method is very convenient to construct a regular hexagon. I've marked the vertices of the hexagon in red.