1. Lesson 6-1
Medians

2. Ohio Content Standards:

3. Ohio Content Standards:
Formally define geometric figures.

4. Ohio Content Standards:
Formally define and explain key aspects of geometric figures, including: a. interior and exterior angles of polygons; b. segments related to triangles (median, altitude, midsegment); c. points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter); d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle).

5. Median

6. Median
A segment that joins a vertex of the triangle and the midpoint of the side opposite that vertex.

7. Median A B D
median BD C

8. A E B D C

9. A E B D C
Find BE if AB = 18.

10. If CD = 2x + 5, BD = 4x – 1, and AE = 5x -2, find BE.

11. Centroid

12. The common point where the medians of a triangle intersect.
Centroid
The common point where the medians of a triangle intersect.

13. Centroid C A B D L E F
centroid

14. Concurrent

15. When three or more lines or segments meet at the same point.
Concurrent
When three or more lines or segments meet at the same point.

16. Theorem 6-1

17. Theorem 6-1
The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.

18. Theorem 6-1 2x x

19. Y N P Q X M Z
Find YQ if QM = 4.

20. Y N P Q X M Z
If QZ = 18, what is ZN?

21. Assignment: Pgs. 231-233 8-18 all, 24-29 all