Brain Strain Find the value of x. x x x xx

Special Segments in Triangles

MedianMedian

Altitude Altitude

Tell whether each red segment is an altitude of the triangle. The altitude is the true height of the triangle.

Perpendicular Bisector

Tell whether each red segment is an perpendicular bisector of the triangle.

Angle Bisector

Drill & Practice Indicate which special triangle segment the red line is based on the picture and markings

20

Points of Concurrency

The intersection of the angle bisectors is called the INCENTER. Equidistant to the sides

The intersection of the altitudes is called the ORTHOCENTER.

The intersection of the medians is called the CENTROID. Vertex to Centroid is Twice as Long as Centroid to Midpoint

The intersection of the perpendicular bisector is called the CIRCUMCENTER. Equidistant to the vertices

Memorize these! MC AO ABI PBCC Medians/Centroid Altitudes/Orthocenter Angle Bisectors/Incenter Perpendicular Bisectors/Circumcenter

Will this work? MC AO ABI PBCC My Cat Ate Our Apples But I Prefer Blue Cheese Crumbles

Special Property of Medians

Theorem Vertex to CENTROID is TWICE as long as CENTROID to MIDPOINT vertex centroid midpoint

A B F X E C D

A B F X E C D

In ABC, AN, BP, and CM are medians. A B M P E C N If EM = 3, find EC. Ex: 1

In ABC, AN, BP, and CM are medians. A B M P E C N If EN = 12, find AN. Ex: 2

In ABC, AN, BP, and CM are medians. A B M P E C N If CM = 3x + 6, and CE = x + 12, what is x? CM = CE + EM Ex: 3