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Objectives: Use properties of midsegment to solve problems

Section 5-1 Triangle Midsegments SPI 32J: identify the appropriate segment of a triangle given a diagram and vs (median, altitude, angle and perpendicular bisector). Objectives: Use properties of midsegment to solve problems. Do Investigation

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Objectives: Use properties of midsegment to solve problems

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  1. Section 5-1 Triangle Midsegments SPI 32J: identify the appropriate segment of a triangle given a diagram and vs (median, altitude, angle and perpendicular bisector) • Objectives: • Use properties of midsegment to solve problems Do Investigation On page 243 Line segment LN is the midsegment of the triangle (connects the midpoint of the two sides) LN = ½ AB

  2. Triangle Midpoint Theorem Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is ½ its length. Length of Midsegment = ½ length of base

  3. Because the perimeter of MNP is 60, you can find NP. MP = YZTriangle Midsegment Theorem 22 = YZSubstitute 22 for MP. 44 = YZMultiply each side by 2. 1 2 1 2 Finding Lengths using Triangle Midpoint Theorem In ∆XYZ, M, N, and P are midpoints. The perimeter of ∆MNP is 60. Find NP and YZ. NP + MN+ MP = 60 Definition of perimeter NP + 24 + 22 = 60 Substitute 24 for MN and 22 for MP. NP + 46 = 60 Simplify. NP = 14 Subtract 46 from each side. Use the Triangle Midsegment Theorem to find YZ.

  4. MN and BC are cut by transversal AB , so AMN and B are corresponding angles. MN || BC by the Triangle Midsegment Theorem, so AMNB because parallel lines cut by a transversal form congruent corresponding angles. m AMN = 75 because congruent angles have the same measure. In AMN, AM = AN, so m ANM = m AMN by the Isosceles Triangle Theorem. m ANM = 75 by substituting 75 for m AMN. Apply Midpoint Theorem Find m AMN and m ANM.

  5. Real World: Apply Midpoint Theorem Indirect Measurement. Kate wants to paddle her canoe across the lake. To determine how far she must paddle, she paced out a triangle counting the number of strides as shown. a. If Kate’s strides average 3.5 ft, what is the length of the longest side of the triangle? b. What distance must Kate paddle across the lake? a. 1050 ft b. 437.5 ft

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