Bell Problem Simplify the expression..

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5.1 Midsegment Theorem & Coordinate Proof

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Presentation transcript:

Bell Problem Simplify the expression.

5.1 Midsegment Theorem and Coordinate Proof Standards: Describe spatial relationships using coordinate geometry Use types of reasoning/methods of proof

Midsegment of a Triangle Midsegment 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

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.

Ex. Triangles are used for strength in roof trusses Ex. Triangles are used for strength in roof trusses. In the diagram, UV and VW are midsegments of ΔRST. Find UV and RS.

Ex. Use ΔGHJ, where A, B, and C are midpoints of the sides Ex. Use ΔGHJ, where A, B, and C are midpoints of the sides. If AC = 3y – 5 and HJ = 4y + 2, what is HB?

Coordinate Proof Ex. Place a rectangle in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex.

Ex. A square has vertices (0, 0), (m, 0), and (0,m) Ex. A square has vertices (0, 0), (m, 0), and (0,m). Find the fourth vertex.

Ex. Find the length of the hypotenuse and the coordinates of an isosceles right triangle’s midpoint M.

Homework pg. 298-299 #4-18 even, 24, 26