Special Segments in Triangles Surrrre they are…

There are 4 special segments in a triangle. segments in a triangle. When all the segments of a type are drawn, they are concurrent (intersect at the same point). The points have special names and special properties. DON’T COPY!!!

Start at a vertex and form a 90° angle with the line containing the opposite side. Orthocenter

The orthocenter can be located in the triangle, on the triangle or outside the triangle. Right Legs are altitudes Obtuse

orthocenter Volunteer?? orthocenter CLICK HERE CLICK HERE

Angle bisectors start at a vertex and bisect the angle. Incenter

The Incenter is equidistance from all 3 sides from all 3 sides

Volunteer?? Incenter CLICK HERE CLICK HERE

A Perpendicular bisector of a side does not have to start at a vertex. It will form a 90° angles and bisect the side. a 90° angles and bisect the side. Circumcenter #3

This makes the Circumcenter an equidistance from the 3 vertices

Volunteer?? CLICK HERE CLICK HERECircumcenter

The median starts at a vertex and ends at the midpoint of the opposite side. Centroid

Volunteer?? CLICK HERE CLICK HERECentroid

Altitude.. Vertex.. 90°.. Orthocenter Vertex.. 90°.. Orthocenter Angle Bisector.. Vertex…split angles.. Incenter Vertex…split angles.. Incenter Perpendicular Bisector… 90°.. bisects side.. Circumcenter 90°.. bisects side.. Circumcenter Median.. Vertex.. Midpoint of side.. Centroid Vertex.. Midpoint of side.. Centroid

Give the best name for AB A B A B A B A B A B || | | || Median Perp Bisector Altitude None None Angle Bisector

Triangle Activity in Plastic Sleeve 1 P QD

2 P Q D

3 P D Q

4 P QD

Back to Notes Special Fact: segment drawn from midpoint to midpoint is half the measure of the parallel side 16 m 8 m X

The centroid is 2/3’s of the distance from the vertex to the side. from the vertex to the side. 2x x X16

If AB = 24, AE = 30, and DZ = 16, find AZ, ZB, AC, CE, EZ, and ED.A B C D E F Z

The centroid is the center of balance for the triangle. You can balance a triangle on the tip of your pencil if you place the tip on the centroid

ELM POST Angle bisector for the streets Perpendicular bisector for houses

Where would you place a fire hydrant to make it equidistance to the houses and equidistance to the streets? ELM POST

Survival Training You’re stranded on a triangular shaped island. The rescue ship can only dock on one side of the island but you don’t know which side. At which point of concurrency would you set up camp so you are an equal distance from all 3 sides? INCENTER

What if the ship could only dock at the verticies? Would you change the location of the camp ? If so, where? YES, CIRCUMCENTER CIRCUMCENTER

The End

Worksheet

BC NM AC True 29. False 30. True