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5.1 Midsegment Theorem & Coordinate Proof

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Objectives Use properties of midsegments Understand coordinate proofs

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Vocabulary The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. D B C E A D and E are midpoints DE is the midsegment

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Theorem 5.1 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. Midsegment Theorem D B C E A DE || AC DE = ½ (AC)

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Example 1 In the diagram, ST and TU are midsegments of PQR. Find PR and TU. PR = ________ TU = ________16 ft 5 ft

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Example 2 In the diagram, XZ and ZY are midsegments of LMN. Find MN and ZY. MN = ________ ZY = ________53 cm 14 cm

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Example 3 In the diagram, ED and DF are midsegments of ABC. Find DF and AB. DF = ________AB = ________2652 3x – 4 5x + 2 x = ________10

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Kinds of Proofs: Two Column Proof has numbered statements and corresponding reasons that show an argument in a logical order. A Flow Proof uses arrows to show the flow of a logical argument. A Coordinate Proof is when you use variables to represent the coordinates of a generic figure to show the results are true for all figures of that type. A Paragraph Proof presents a logical argument as a written explanation in paragraph form.

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EXAMPLE 3 Place a figure in a coordinate plane Place each figure in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex. a. A rectangle b. A scalene triangle SOLUTION It is easy to find lengths of horizontal and vertical segments and distances from (0, 0), so place one vertex at the origin and one or more sides on an axis. Example 4

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EXAMPL 3 a. Let h represent the length and k represent the width. b. Notice that you need to use three different variables. Example 4 (continued)

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Assignment Workbooks Pg. 85 - 87 #1 – 18, 20

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