1. 5.1 MidsegmentTheorem & Coordinate Proof

2. Objectives • Use properties of midsegments • Understand coordinate proofs

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

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

5. Example 1 In the diagram, ST and TU are midsegments of PQR. Find PR and TU. 5 ft 16 ft TU = ________ PR = ________

6. Example 2 In the diagram, XZ and ZY are midsegments of LMN. Find MN and ZY. 14 cm 53 cm ZY = ________ MN = ________

7. 5x + 2 3x – 4 Example 3 In the diagram, ED and DF are midsegments of ABC. Find DF and AB. x = ________ 10 DF = ________ 26 AB = ________ 52

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

9. A rectangle A scalene triangle a. b. 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 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.

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

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