Review of Perpendicular and Angle Bisectors in Triangles

Bisectors and Centers of Triangles

Let's see if we can tell the difference between the different centers of triangles!

Perpendicular Bisectors

• Equidistant from the vertices of the triangle

• The three perpendicular bisectors of each side meet at the circumcenter

Circumcenter

Incenter

• Equidistant from the sides of the triangle

• The three angle bisectors of each vertex meet at the incenter

Angle Bisectors

Centroid

• 2/3rds of the way from the vertices of the triangle to the midpoint of the opposite side (medians)

• Because we know the midpoint's location for each side, we know that on either side of the midpoint, the segments are congruent.

• Can also be found by taking the average of all the vertices

Medians

Orthocenter

• Where at least 2 perpendicular lines from the vertices of the triangle to the opposite side (altitudes) meet.

• The orthocenter of an obtuse triangle is the only center that's OUTSIDE the triangle itself!

Altitudes

Multiple Choice

What is being shown in this diagram?

• Circumcenter

• Incenter

• Centroid

• Orthocenter

Multiple Choice

What is being shown in this diagram?

• Circumcenter

• Incenter

• Centroid

• Orthocenter

Multiple Choice

What is being shown in this diagram?

• Circumcenter

• Incenter

• Centroid

• Orthocenter

Multiple Choice

What is being shown in this diagram?

• Circumcenter

• Incenter

• Centroid

• Orthocenter