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?

• Show Step-by-step Solutions

How to construct a 60 degree angle using only a compass and straight edge?

• Show Step-by-step Solutions

How to construct an equilateral triangle?

• Show Step-by-step Solutions

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.
   

• Show Step-by-step Solutions

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