Special Lines in a Triangle

Jill Chittenden, Nov 24, 2020

This activity will explore the lines in a triangle and their points of concurrency.


  • 1. Perpendicular Bisectors
  • 2. Angle Bisectors
  • 3. Medians
  • 4. Altitudes
  • 5. Bonus: Euler's Line

1.

Perpendicular Bisectors

Perpendicular Bisectors
A perpendicular bisector intersects a side of a triangle at its midpoint and makes a right angle with the side. Drag the vertices of the triangle below to explore the perpendicular bisector.
All three perpendicular bisectors meet at a point. This is called a point of concurrency, which is when three or more lines intersect at the same point. The point of concurrency for the perpendicular bisectors is called the circumcenter. Can the circumcenter be outside the triangle? If so, when?
Using the triangle above, create segments from the circumcenter (D) to each vertex (A, B and C). Then use the measure tool to find the length of each of those segments. Move the vertices around. What did you find?
– Jill Chittenden

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