1. Warm Up 12.01.11 Week 7

2. Geometry 5.3 Day 1 I will use properties of medians of a triangle. A segment with endpoints on a vertex and the midpoint of the opposite side. There are 3 medians. Median of a Triangle Ex 1 Midpoint Vertex Median

3. Ex 2 Where the 3 medians meet inside the triangle. Centroid

4. Concurrency of Medians of a Triangle The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. Theorem 5.7 P D A AP = AD PD = AD B C E F

5. Ex 3 P is the Centroid of ∆ QRS. P Q R S T PT = 5 Find RT and RP. 5 PT = RT ( 5 ) = RT ( 3 ) 15 = RT RP = 10 RP = RT RP = ( 15 )

6. The perpendicular distance between a vertex and the opposite side. It can be in, on or outside the triangle. Altitude Triangles have 3 altitudes. Rule 1 Ex 4

7. Ex 5Find the Centroid. K ( 5, 2 ) L ( 3, 6 ) J ( 7, 10 ) N M 1) Find Midpoint LJ M = M = ( 5, 8 ) 2) Find distance from K to N ( 5, 8 ) KN = 8 - 2 KN = 6 6 P 3) Find distance from K to P KP = ( 6 ) KP = KN KP = 4up from the vertex. 4) Find the centroid P = ( 5, 4 + 2 ) 2 P = ( 5, 6 )

8. Do 1 : What is the length of QC and CP? P Q R S B A C 12 Handout - 5.3B Assignment

9. Ex 5Find the Centroid. K ( 5, 2 ) L ( 3, 6 ) J ( 7, 10 ) N M 1) Find a Midpoint M = M = ( 5, 8 ) 2) Find distance from K to N ( 5, 8 ) KN = 8 - 2 KN = 6 6 P 3) Find distance from K to P P = ( 6 ) P = KN P = 4up from the vertex. 4) Find the centroid M = ( 5, 4 + 2 ) 2 M = ( 5, 6 )