1. Geometry 5-3b Medians and Altitudes

2. Definitions Median of a triangle – a segment whose endpoints are a vertex and the midpoint of the opposite side Altitude of a triangle – A perpendicular segment from a vertex to the line containing the opposite side of the triangle

3. Investigation Calculators

4. Calculator Investigation Turn the calculator ON, and start a new file Home > 1 > no > Open a graphs and geometry view window (3)

5. Calculator Investigation Create a triangle, by connecting three line segments, label the segments CNR Line segments are MENU > 7 > 5 Add a label with Cntrl > Menu > 2

6. Calculator Investigation Construct the midpoints of each triangle side Midpoints are MENU > A > 5

7. Calculator Investigation Construct medians, connecting midpoints to the opposite vertex Segments are MENU > 7 > 5

8. Calculator Investigation Construct the intersecting points to find the centroid, label it T Intersecting points are MENU > 7 > 3

9. Median Concurrancy The three medians of a triangle are concurrent Centroid

10. Calculator Investigation Measure the short and the long part of a median Measuring is MENU > 8 > 1

11. Calculator Investigation What do you notice about the two lengths? Alter the shape of the triangle, does this still hold?

12. Centroid Theorem The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.

13. Investigation Cardboard Scissors Ruler / Straight Edge Straightedge

14. Investigation Cut out a scalene triangle Draw all medians onto the triangle Try balancing the cardboard triangle on your ruler edge, along a median

15. Investigation Find the centroid for your triangle

16. Investigation Try balancing your triangle on the eraser of your pencil at the centroid

17. Center of Gravity Conjecture The centroid of a triangle is the center of gravity of the triangular region

18. Summary

19. Practice

21. Homework Pages 260 – 262 11 – 16, 20, 22, 27 – 29

22. Honors Homework Pages 260 – 262 11 – 16, 20, 22, 27 – 29, 34