An equilateral triangle is a classical geometric figure, characterized by three sides of equal length and by the respective three angles of equal width. Drawing a perfect freehand one can be difficult; using a circular object to draw the corners and a ruler to draw perfectly straight lines will therefore simplify the process. Read on to find out how to draw an equilateral triangle.
Steps
Method 1 of 3: Using a Compass
Step 1. Draw a straight line
Place the ruler on a sheet of paper, then use the pencil to draw a straight line. The segment just traced represents one of the three sides of the figure, consequently it is necessary to trace two other lines of the same length, oriented however so as to form two angles of 60 ° with the first. Make sure there is enough space on the paper to allow you to draw all three sides of your triangle.
Step 2. Open the compass using the segment just drawn as a reference
If you are using a pencil compass, proceed by inserting the pencil into the holder and make sure it is well pointed. Place the tip of the compass exactly at one end of the segment, then open it so that the tip of the pencil coincides perfectly with the other end.
Step 3. Draw an arc that is a quarter of a circumference wide
Do not move the tip of the compass away from the end of the segment in which it is positioned and do not change its opening. Proceed to draw an arc upwards that has a length equal to a quarter of a circumference.
Step 4. Place the tip of the compass on the second end of the segment
Do this without modifying the opening of the tool in the slightest.
Step 5. Draw a second arc
With a light hand, draw a second arc so that it intersects the one drawn in the previous step.
Step 6. Highlight the intersection point of the two arcs
This is the vertex of the equilateral triangle we are drawing. If projected onto the starting segment, the intersection point should fall exactly in the center, dividing it perfectly in half. Now you are able to draw the other two sides of the triangle, joining the vertex with the two ends of the first drawn segment.
Step 7. Complete the triangle
Use a ruler to trace the two missing sides of the figure. Connect the two ends of the original segment with the vertex identified in the previous step (the intersection point of the two arcs). Make sure the lines are perfectly straight. To complete the drawing, erase the construction lines so that only the three sides of the triangle are visible.
- Consider moving the triangle back to a new page by tracing it. This way you will get a perfect figure, with no trace of the related construction lines.
- If you need to draw a larger or smaller figure, you simply need to change the length of the starting segment used as a base. The greater the length, the larger the full figure will turn out.
Method 2 of 3: Use a Circular Base Object
If you don't have a compass or protractor, you can use any object that has a circular base. This method is basically the same as that of the compass, but in this case you need to be a little creative.
Step 1. Choose a circular object
You can use virtually any cylindrical object with a circular base, such as a bottle or can. Try using a roll of duct tape or a CD. Since you will have to trace the two arcs that would normally be drawn with the compass, the chosen object must have the right dimensions. In this case each side of the triangle will be exactly as long as the radius (half the diameter) of the selected circular object.
If you're using a CD: Imagine you see a circumscribed equilateral triangle within the upper right quadrant of the disc
Step 2. Draw the first side
It should be exactly as long as the radius of the circular object you are using, i.e. equal to the distance between the center and any point on the circumference. Make sure you draw a perfectly straight line.
- If you have a ruler, simply measure the diameter of the object you are using and draw a straight line that is half as long.
- If you don't have a ruler, place the circular object on the sheet of paper, then very carefully trace the circumference using a pencil. When finished, remove the object, you should be able to admire a perfect circle. Use an object that has a straight side to draw a line that passes exactly through the center of the circle; the latter is the point equidistant from any other point positioned on the circumference.
Step 3. Use the circular object to draw an arc
Place the circular object on the base segment, so that one of the two ends coincides with the center. Be careful in this step and make sure that the end of the basic line coincides perfectly with the center of the circle. Use a pencil to draw an arc that is about a quarter of the way around the object.
Step 4. Draw the second arc
Now move the circular object so that the center coincides perfectly with the other end of the base segment. Again, accuracy is very important. Draw a second arc that intersects the first at a point above the base segment. The identified point represents the vertex of the triangle.
Step 5. Complete the triangle
Draw the remaining sides of the figure. Connect the two ends of the base segment with the vertex found in the previous step. Make sure the lines are perfectly straight. As a result you should have obtained a perfect equilateral triangle.
Method 3 of 3: Using a Protractor
Step 1. Draw the first side
To do this, use a ruler or protractor base. Draw a line of the desired length. This segment represents the first side of the triangle and the other two must have the same length. If you are doing precision work, make sure this first line is the correct size.
Step 2. Use the protractor to measure a 60 ° angle at one end of the base segment
Step 3. Trace the second side
Our goal is to get a second straight line that is perfectly identical to the first. Start from the end where you measured the 60 ° angle. Starting at the vertex of the corner, draw a straight line that is exactly as long as the base segment and forms a 60 ° angle with it.
Step 4. Complete the triangle
Use the base of the protractor to trace the third side of the triangle. Connect the second end of the line drawn in the previous step with the remaining free end of the base segment. Again you should have obtained a perfect equilateral triangle.
Advice
- Although it does not rely on the correct measurement of angles, drawing a triangle using the compass usually leads to a more accurate result.
- Try to draw light lines when using the compass, being construction lines at the end they will be erased; in this way, eliminating them will be much easier.
- Use a compass equipped with an opening lock to avoid the risk of inadvertently changing it during use.
