Construct a 60˚Angle by Constructing An Equilateral Triangle
In this lesson, we will learn
- how to construct a 60 degrees angle.
- how to construct an equilateral triangle.
- how to Inscribe a Regular Hexagon in a Circle.
- how to Inscribe an Equilateral Triangle in a Circle.
Go through the steps below to construct an equilateral triangle. Pick any length for a side of the equilateral triangle.
Example :
Construct 
= 60˚.
Solution:
Step 1 : Mark the point B on the line.
Step 2 : Stretch the compasses to any width. Put the sharp end of the compasses at point B and draw an arc on the line. Label the point where the arc intersects the line as point C.
Step 3: While keeping the sharp end of the compasses at point B, move the compasses away from C and draw a second arc above the line about mid-way between points B and C.
Step 4: Without changing the width of the compasses, place the sharp end of the compasses at point C and draw an arc to intersect the second arc.
Step 5 : Draw a line from point B to the point of intersection of the 2 arcs. Label the angle 60˚.
How to Inscribe a Regular Hexagon in a Circle?
1. Measure the distance of the circle's radius.
2. Plot a point on the circle.
3. Starting from that point, use the compass to measure the distance of the radius and make an arc intersecting the circle.
4. Repeat step 3 around the circle until you return to the original point.
5. Connect the six points to form a hexagon.
How to Inscribe an Equilateral Triangle in a Circle?
1. Inscribe a hexagon in the circle.
2. Connect every other point on the hexagon to form an equilateral triangle.
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