1. 5.4 Use Medians and Altitudes.

2. Vocabulary… Concurrent- 3 or more lines, rays, or segments that intersect at the same point Median of a Triangle – a segment from a vertex to the midpoint of the opposite side Centroid – point of concurrency of 3 medians Altitude of a Triangle – the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side – there are 3 in a

3. Median of a Triangle A Median of a triangle is a segment that connects the vertex to the midpoint of the opposite side. A BC D

4. Center of Gravity The centroid is found at the point of concurrency of the medians of a triangle. known as the center of gravity A B C Balance Point

5. Altitude- height

6. Centroid Theorem Maybe we should call it the median theorem? Either For any median, from the vertex to the centroid is 2/3 the distance of the median A B C D E

7. L is the centroid of  MNO NP = 11, ML = 10, NL = 8 PO = _____ 11

8. L is the centroid of  MNO NP = 11, ML = 10, NL = 8 MP = _____ 15 5

9. L is the centroid of  MNO NP = 11, ML = 10, NL = 8 LQ = _____ 4

10. 3 1 =  bisector 2 = angle bisector 3 = a median 4 = an altitude 2 4 1, 2, 3, and 4

11. http://www.khanacademy.org/math/geometry/triangl e-properties/triangle_property_review/v/review-of- triangle-properties