Triangle Centers

Diana Braun, Oct 3, 2016

Discover the triangle centers and their properties

Table of Contents

  1. The Three Little Medians
    1. Three Little Medians
  2. Goldilocks and the Three Altitudes
    1. Three Altitudes
  3. Three Blind Perpendicular Bisectors
    1. Three Perpendicular Bisectors
  4. The Tale of the Three Angle Bisectors
    1. Three Angle Bisectors
  5. The Legend of Euler
    1. Euler Segment

1.

The Three Little Medians

Where do the 3 medians of a triangle meet?

  • 1. Three Little Medians

1.1.

Three Little Medians

Click on the check boxes to see where the three medians of a triangle meet.
Look at the distnace from the vertex to the centroid vs. the distance from the centroid to the midpoint. What do you notice?
– Diana Braun

2.

Goldilocks and the Three Altitudes

See where the three altitudes meet

  • 1. Three Altitudes

2.1.

Three Altitudes

Click on the Check boxes to see where the 3 altitudes meet.
Click and drag on a point to make the triangle acute, obtuse, and right. Where is the orthocenter located?
– Diana Braun

3.

Three Blind Perpendicular Bisectors

See where the perpendicular bisectors meet

  • 1. Three Perpendicular Bisectors

3.1.

Three Perpendicular Bisectors

Click on the check boxes to see where the perpendicular bisecotrs meet.
What is the circumcenter the "center" of? What are it's properties?
– Diana Braun

4.

The Tale of the Three Angle Bisectors

See where the angle bisectors meet.

  • 1. Three Angle Bisectors

4.1.

Three Angle Bisectors

Click on the check-boxes to see where the anlge bisectors meet.
What is the Incenter the "center" of?
– Diana Braun

5.

The Legend of Euler

  • 1. Euler Segment

5.1.

Euler Segment

Click and drag the vertices of the triangle to make acute, obtuse, isosceles, and equilateral triangles. What do you notice about the centers of the triangle?
– Diana Braun

Information