# 5.1 – Midsegment Theorem and Coordinate Proof

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5.1 – Midsegment Theorem and Coordinate Proof
A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle. Every triangle has three midsegments. The midsegments of Triangle ABC at the right are Segment MP, Segment MN, and Segment NP.

5.1 – Midsegment Theorem and Coordinate Proof

5.1 – Midsegment Theorem and Coordinate Proof
Example 1: Triangles are used for strength in roof trusses. In the diagram, Segment UV and Segment VW are midsegments of Triangle RST. Find UV and RS.

5.1 – Midsegment Theorem and Coordinate Proof
Example 2: In the diagram of an A-frame house, Segment DG and Segment DH are midsegments of Triangle ABF. Find DG and BF.

5.1 – Midsegment Theorem and Coordinate Proof
A coordinate proof involves placing geometric figures in a coordinate plane. When you use variables to represent the coordinates of a figure in a coordinate proof, the results are true for all figures of that type.

5.1 – Midsegment Theorem and Coordinate Proof
Example 4: Place each figure in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex. A rectangle b. A scalene triangle c. An isosceles triangle d. A square

5.1 – Midsegment Theorem and Coordinate Proof
Example 5: Place an isosceles right triangle in a coordinate plane. Then find the length of the hypotenuse and the coordinates of its midpoint M.

5.1 – Midsegment Theorem and Coordinate Proof
Example 5:

5.1 – Midsegment Theorem and Coordinate Proof
Example 5: