How to Construct the Altitude of a Triangle With a Compass


A triangle is a closed two-dimensional shape with three sides and three angles. There are a wide variety of triangles, including acute ones, with all the angles less than 90 degrees; obtuse triangles, with one angle larger than 90 degrees; and equilaterals, with all sides and angles equal. In geometry, a compass is a v-shaped tool with a sharp point on one end and a drawing tip, such as a pencil, on the other. When the pencil rotates around the secure point, the compass makes a circle.

Things You'll Need

  • Compass
  • Straight edge
  • Spread the two ends of the compass 2 inches apart.

  • Press the point into the paper and rotate the pencil around the point. This creates a 4-inch circle.

  • Move the compass to the right. Place the point of the compass on the line of the circle. Draw a second circle that crosses the first. The line of the new circle crosses the center point of the original circle.

  • Move the compass toward the top of the paper, between the two circles. Place the pencil on the center point of the second and press the point into the paper. Lift the pencil and, with the point still secured, place it on the center point of the first circle. If the pencil doesn't fit, do not spread the compass but move the point. Shift the point of the compass until the pencil touches the center point of both circles. Rotate the pencil to draw a third circle. You now have three intersecting triangles.

  • Lay the straight edge to connect the center points of two circles. Draw a line connecting the two points. Repeat, connecting all three center points of the circle. This gives you an equilateral triangle.

  • Lay the straight edge so that it bisects the top angle of the triangle. This is the center point of the top circle. Slide the bottom of the straight edge so that it lines up with the point where the other two circles cross. Draw a line from the angle of the triangle to the opposite side of the triangle. This line is perpendicular to the side of the triangle. This is the altitude of the triangle.

  • Repeat Step 6 for the other two angles.

Tips & Warnings

  • The point at which all three altitudes cross is called the centroid.
  • Be careful with the sharp end of the compass. Do not press the sharp end into the paper so hard that you damage the work surface beneath. If in doubt, place your paper on cardboard to protect the work surface.

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  • Photo Credit Stockbyte/Stockbyte/Getty Images
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