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Chapter 6: More about Triangles 6-1: Medians

Chapter 6: More about Triangles 6-1: Medians. 6-1: Medians. Median : A segment that joins a vertex of the triangle at the midpoint of the side opposite that vertex. The median splits the side into two equal parts. 6-1: Medians. F. Example 1 In EFG, FN is a median. Find EN if EG = 11.

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Chapter 6: More about Triangles 6-1: Medians

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  1. Chapter 6: More about Triangles6-1: Medians

  2. 6-1: Medians • Median: A segment that joins a vertex of the triangle at the midpoint of the side opposite that vertex. • The median splits the side into two equal parts

  3. 6-1: Medians F • Example 1 • In EFG, FN is a median. • Find EN if EG = 11. • If FN is a median, then N isa midpoint of EG • If EG = 11, then EN is (left) half • EN = ½  11 = 5.5 N E G

  4. 6-1: Medians • Your Turn • In MNP, MC and ND are medians. • What is NC if NP = 18? • 9 • If DP = 7.5, find MP. • 15 • If PD = 7x – 1, CP = 5x – 4, and DM = 6x + 9, find NC. • 46

  5. 6-1: Medians • Centroid: The point where all three medians of a triangle intersect. • Concurrent: When three or more lines or segments meet at the same point. • X is the centroidof JKM. • QM, JR, and PKare concurrent.

  6. 6-1: Medians • There is a unique relationship between the length of a segment from the centroid to the vertex and from the centroid to the midpoint. • See the examples below.

  7. 6-1: Medians • Theorem 6-1: The length of a segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint. • Note this means: • Centroid to midpoint = 1/3 of whole median • Centroid to vertex = 2/3 of whole median

  8. 6-1: Medians • Example 2 • In XYZ, XP, ZN, and YM are medians. • Find ZQ if QN = 5. • ZQ is centroid to vertex • It’s twice as long as centroid to midpoint • ZQ = 2  5 = 10 • If XP = 10.5, what is QP? • QP is centroid to midpoint • It’s half the length of centroid to vertex (no good) • It’s 1/3rd the entire length of the median • QP = 1/3 10.5 = 3.5

  9. 6-1: Medians • Your Turn • In ABC, AE, BF and CD are medians. • If CG = 14, what is DG? • 7 • Find BF if GF = 6.8? • 20.4

  10. 6-1: Medians • Assignment • Worksheet #6-1

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