2 ObjectivesUse properties of midsegmentsUnderstand coordinate proofs
3 VocabularyThe Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle.DBCEAD and E are midpointsDE is the midsegment
4 Midsegment Theorem 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.DBCEADE || ACDE = ½ (AC)
5 Example 1 5 ft 16 ft TU = ________ PR = ________ In the diagram, ST and TU are midsegments of PQR. Find PR and TU.5 ft16 ftTU = ________PR = ________
6 Example 2 14 cm 53 cm ZY = ________ MN = ________ In the diagram, XZ and ZY are midsegments of LMN. Find MN and ZY.14 cm53 cmZY = ________MN = ________
7 Example 3 x = ________ 10 DF = ________ 26 AB = ________ 52 In the diagram, ED and DF are midsegments of ABC. Find DF and AB.3x – 45x + 2x = ________10DF = ________26AB = ________52
8 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 Paragraph Proof presents a logical argument as a written explanation in paragraph form.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.
9 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.a.A rectangleb.A scalene triangleSOLUTIONIt 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.
10 Example 4 (continued) EXAMPL 3 a. Let h represent the length and k represent the width.b.Notice that you need to use three different variables.