TRIANGLE RELATIONSHIPS Math Alliance November 16, 2010.

TRIANGLE RELATIONSHIPSMath AllianceNovember 16, 2010

Triangle Relationship #1

Draw a triangle on a piece of patty paper

Find the perpendicular bisector of one side of your triangle Perpendicular = Bisector =

What strategies did you use to find the perpendicular bisector?

Triangle Relationship #1 (Contd.)

Find the perpendicular bisectors of the other two sides of your triangle

What do you observe?

Compare with others at your table, and make a conjecture

Triangle Relationship #1 (Contd.)

Choose one of your perpendicular bisectors

What is special about the points on that perpendicular bisector?

What is special about the point of concurrency of the perpendicular bisectors?

The Circumcenter

The point at which the three perpendicular bisectors of the sides are concurrent.

The point which is equidistant from all three vertices of the triangle

The center of the circle which passes through all three vertices (the circumcircle).

Triangle relationship #2

Draw a different triangle on a new piece of patty paper.

Find one of the medians of your triangle. Median =

What strategies did you use to find the median?

Triangle relationship #2 (Contd.) Find the other two

medians of your triangle.

What do you observe?

Compare with others at your table and make a conjecture.

Triangle relationship #2 (Contd.) Trace your triangle,

and all three medians, onto a piece of card stock.

Carefully cut out the cardstock copy of your triangle.

Try to balance your triangle on a pencil or compass point.

The Centroid

What does this give you?

Triangle relationship #3

The Orthocenter

The point at which the three altitudes are concurrent. Altitude =

Triangle relationship #4

The Incenter

The point at which the three angle bisectors concurrent. Angle Bisector =

The Euler Line

The line that contains the: Centroid Orthocente

r Circumcent

er

Homework

Section 10.21-6, 10, 17, 19, 23-25, 34Turn in #’s 10, 23-25 (pick one), and 34