TRIANGLE RELATIONSHIPS Math Alliance November 16, 2010.
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Transcript of TRIANGLE RELATIONSHIPS Math Alliance November 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.
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 =