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.
We now construct a 60˚ angle by constructing an equilateral triangle. Recall that the angles in an equilateral triangle are 60˚.
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 construct a 60 degree angle and an equilateral triangle?
How to construct a 60 degree angle using only a compass and straight edge?
How to construct an equilateral triangle?
How to Inscribe a Regular Hexagon in a Circle?
- Measure the distance of the circle’s radius.
- Plot a point on the circle.
- Starting from that point, use the compass to measure the distance of the radius and make an arc intersecting the circle.
- Repeat step 3 around the circle until you return to the original point.
- Connect the six points to form a hexagon.
How to Inscribe an Equilateral Triangle in a Circle?
- Inscribe a hexagon in the circle.
- Connect every other point on the hexagon to form an equilateral triangle.
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