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Bell Problem
Simplify the expression.
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5.1 Midsegment Theorem and Coordinate Proof
Standards:1. Describe spatial relationships using coordinate
geometry2. Use types of reasoning/methods of proof
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Midsegment of a TriangleMidsegment of a triangle- a segment that connects the midpoints of two sides of the triangle
• Every triangle has three midsegments • The midsegments of ΔABC are
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Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.
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Ex. Triangles are used for strength in roof trusses. In the diagram, UV and VW are midsegments of ΔRST. Find UV and RS.
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Ex. Use ΔGHJ, where A, B, and C are midpoints of the sides. If AC = 3y – 5 and HJ = 4y + 2, what is HB?
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Coordinate ProofEx. Place a rectangle in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex.
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Ex. A square has vertices (0, 0), (m, 0), and (0,m). Find the fourth vertex.
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Ex. Find the length of the hypotenuse and the coordinates of an isosceles right triangle’s midpoint M.
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Homework
pg. 298-299 #4-18 even, 24, 26