Presentation on theme: "Do Investigation On page 243"— Presentation transcript:
1 Do Investigation On page 243 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 problemsDo InvestigationOn page 243Line segment LN is the midsegment of the triangle(connects the midpoint of the two sides)LN = ½ AB
2 Triangle Midpoint Theorem Triangle Midsegment TheoremIf 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 Finding Lengths using Triangle Midpoint Theorem In ∆ XYZ, M, N, and P are midpoints. The perimeter of ∆ MNP is 60. Find NP and YZ.Because the perimeter of MNP is 60, you can find NP.NP + MN + MP = 60 Definition of perimeterNP = 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.MP = YZ Triangle Midsegment Theorem22 = YZ Substitute 22 for MP.44 = YZ Multiply each side by 2.12
4 Apply Midpoint Theorem Find m AMN and m ANM.MN and BC are cut by transversal AB , so AMN andB are corresponding angles.MN || BC by the Triangle Midsegment Theorem, soAMN B because parallel lines cut by a transversalform congruent corresponding angles.m AMN = 75 because congruent angles have thesame measure.In AMN, AM = AN, so m ANM = m AMN by the IsoscelesTriangle Theorem.m ANM = 75 by substituting 75 for m AMN.
5 Real World: Apply Midpoint Theorem Indirect Measurement. Kate wants to paddleher canoe across the lake. To determine howfar she must paddle, she paced out a trianglecounting 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 ftb ft