How Do You Find the Perpendicular Bisector of a Triangle?

perpendicular-bisector-triangle Credit: Peter Unger/Lonely Planet Images/Getty Images

A perpendicular bisector is a line that divide another line into two equal measures and is perpendicular to the line it dissects. A triangle has three perpendicular bisectors, one for each side. To find the perpendicular bisector, which is not immediately visible, you need to measure a side to find the point that divides it into equal halves, and then draw a line that passes through that point and creates a right angle with the side.

  1. Measure a side

    Find the length of a side of any triangle using a ruler. You need this value to find out where the midpoint lies on that side.

  2. Find the midpoint

    Divide the side's length in half. From an endpoint of the same side, measure that half-length and mark it. That is the midpoint of the side.

  3. Construct the perpendicular line

    Draw a line that forms a 90-degree angle with the side of the triangle and passes through its measured midpoint. Use a protractor to ensure that the angle you're creating is a perfect right angle. This line is the side's perpendicular bisector.

  4. Find the perpendicular bisectors for the other sides

    Repeat the process for the other sides of the triangle. All triangles have three perpendicular bisectors, regardless of type or size.