1. TRIANGLE RELATIONSHIPS Math Alliance November 16, 2010

2. 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?

3. 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

4. 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?

5. 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).

6. 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?

7. 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.

8. 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.

9. The Centroid  What does this give you?

10. Triangle relationship #3  The Orthocenter  The point at which the three altitudes are concurrent.  Altitude =

11. Triangle relationship #4  The Incenter  The point at which the three angle bisectors concurrent.  Angle Bisector =

12. The Euler Line  The line that contains the:  Centroid  Orthocenter  Circumcenter

13. Homework  Section 10.2  1-6, 10, 17, 19, 23-25, 34  Turn in #’s 10, 23-25 (pick one), and 34