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##### 5.1 Midsegments of Triangles

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**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).**Today’s Agenda**• Chapter 5 Relationships Within Triangles • Triangle Midsegments • Test Make-up**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**Discovery**• What relationships did you discover between a triangle midsegment and the third side of a triangle?**Triangle Midsegment Theorem**• The midsegment of a triangle is half the length of the third side of a triangle. • DE = 5 • BC = 10**Triangle Midsegment Theorem**• The midsegment of a triangle is parallel to the third side of a triangle. • DE || BC**Example 1**• Which segments are parallel?**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**Homework**• 5.1 Worksheet • pg 262 #1 – 13 all**#1**• CD = 4 cm MO = • CE = 8 cm NO = • DE = 7 cm NM =**#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