How to Construct an Equilateral Triangle

An equilateral triangle is a triangle with all three sides equal in length and all three angles measuring 60°. Here’s a step-by-step guide to constructing one using a compass and straightedge (ruler).

Materials Needed:

  • A ruler (straightedge)
  • A compass
  • A pencil
  • A sheet of paper

Steps:

  1. Draw the Base Segment (AB):
  • Use a ruler to draw a straight line segment of your desired length. Label the endpoints as A and B.
  1. Set the Compass:
  • Adjust the compass to the length of AB.
  1. Draw an Arc from Point A:
  • Place the compass at point A and draw an arc above the line segment.
  1. Draw an Arc from Point B:
  • Without changing the compass width, place it at point B and draw another arc that intersects the first arc.
  1. Mark the Third Vertex (C):
  • The intersection point of the two arcs is the third vertex of the triangle, C.
  1. Complete the Triangle:
  • Use the ruler to draw lines from A to C and from B to C.

Now, you have a perfect equilateral triangle (△ABC) with all sides and angles equal!

Verification:

  • Measure all three sides—they should be equal.
  • Use a protractor to confirm that each angle is 60°.

Author

Leave a Comment