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5.1 Midsegments of Triangles

5.1 Midsegments of Triangles. Brett Solberg AHS ’11-’12. Warm-up 11-28-2011. 1) Find the distance between (1, 4) and (4,8). 2) Find the midpoint of the segment whose endpoints are (4, 11) and (6, 3). 3) Find the slope of the line containing the points (8, 3) and (7, 12).

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5.1 Midsegments of Triangles

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  1. 5.1 Midsegments of Triangles Brett Solberg AHS ’11-’12

  2. Warm-up 11-28-2011 • 1) Find the distance between (1, 4) and (4,8). • 2) Find the midpoint of the segment whose endpoints are (4, 11) and (6, 3). • 3) Find the slope of the line containing the points (8, 3) and (7, 12).

  3. Today’s Agenda • Chapter 5 Relationships Within Triangles • Triangle Midsegments • Test Make-up

  4. Midsegment of a Triangle • A line that connects two midpoints of two sides of a triangle is called the midsegment of a triangle. • DE is a midsegment of ∆ABC

  5. Discovery • What relationships did you discover between a triangle midsegment and the third side of a triangle?

  6. Triangle Midsegment Theorem • The midsegment of a triangle is half the length of the third side of a triangle. • DE = 5 • BC = 10

  7. Triangle Midsegment Theorem • The midsegment of a triangle is parallel to the third side of a triangle. • DE || BC

  8. Example 1 • Which segments are parallel?

  9. Example 3 • M, N, and P are midpoint in ∆XYZ. The perimeter of ∆MNP is 60. Find NP and YZ. • MN = 22 MP = 24 • MN + MP + NP = 60 • 22 + 24 + NP = 60 • NP = 14 • XY = 28 • YZ = 44 • XZ = 48

  10. Homework • 5.1 Worksheet • pg 262 #1 – 13 all

  11. #1 • CD = 4 cm MO = • CE = 8 cm NO = • DE = 7 cm NM =

  12. #7 • Find the value of the variable. • Perimeter of ∆ABC = 32 cm • n + 7/8n + 1/2n = 32 • 8n + 7n + 4n = 256 • 19n = 256 • n = 13.47

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