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˚.

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.

1. Inscribe a hexagon in the circle.

2. Connect every other point on the hexagon to form an equilateral triangle.

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