5.1 Midsegment Theorem and Coordinate Proof Goal Use properties of midsegments and write coordinate proofs. Day 1: VOCABULARY Midsegment of a triangle ________________________________________________________________________ ________________________________________________________________________ Coordinate proof ________________________________________________________________________ ________________________________________________________________________ THEOREM 5.1: MIDSEGMENT THEOREM The segment connecting the midpoints of two sides of a triangle is __________ to the third side and is ______ as long as that side. Example 1 Use the Midsegment Theorem to find lengths Windows A large triangular window is segmented as shown. In the diagram, DF and EF are midsegments of ABC. Find DF and AB. Checkpoint 1. In Example 1, consider ADF. What is the length of the midsegment opposite DF ? _________________________________________________________________ _________________________________________________________________ Example 2 Use the Midsegment Theorem In the diagram at the right, QS = SP and PT = TR. Show that QR ST . S 2. In Example 2, if V is the midpoint of QR , what do you know about SV ? Extra Practice: MP a midsegment of LNO. Find the value of x. 1 3. 2. 4. In DEF, EJ JF , KF FD and DG GE . Copy and complete the statement. 5. 6. 7. 8. GJ ║__?__ EJ __?__ __?__ DE ║ __?__ GJ __?__ __?__ 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 square b. an acute triangle Example 4 Apply variable coordinates In Example 3 part (a), find the length and midpoint of a diagonal of the square. Extra Practice Use the graph shown. 1. Find the coordinates of the endpoints of each midsegment of PQR. Place the figure in a coordinate plane. Assign coordinates to each vertex. 2. A 4 unit by 7 unit rectangle with one vertex at (0, 0). 3. A square with side length s and one vertex at (s, 0). Hmwrk: pg 298 1, 3-11 all 12,14, 47,48,50,51,52