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Warm Up

Week 7. Warm Up. 12.01.11. Median of a Triangle. A segment with endpoints on a vertex and the midpoint of the opposite side. There are 3 medians. Vertex. Ex 1. Median. Midpoint. Centroid. Where the 3 medians meet inside the triangle. Ex 2. •. Centroid. Theorem 5.7. B. D. E. P.

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Warm Up

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  1. Week 7 Warm Up 12.01.11

  2. Median of a Triangle A segment with endpoints on a vertex and the midpoint of the opposite side. There are 3 medians. Vertex Ex 1 Median Midpoint

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

  4. Theorem 5.7 B D E P PD = AD A C F AP = AD

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

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

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

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

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

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