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).
Table of Contents
Materials Needed:
- A ruler (straightedge)
- A compass
- A pencil
- A sheet of paper
Steps:
- 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.
- Set the Compass:
- Adjust the compass to the length of AB.
- Draw an Arc from Point A:
- Place the compass at point A and draw an arc above the line segment.
- 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.
- Mark the Third Vertex (C):
- The intersection point of the two arcs is the third vertex of the triangle, C.
- 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°.
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