Report

M IDSEGMENTS OF T RIANGLES Honors Geometry Vocabulary Midsegment of a triangle – a segment connecting the midpoints of two sides of the triangle. Midsegment Investigation # Length & slope of midsegment Slope Length Length & slope of triangle side Slope Length 1 2 3 Geogebra Exploration Theorem Triangle Midsegment Theorem- If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half as long. Vocabulary Coordinate Proof – Using coordinate geometry and algebra to prove a hypothesis. We can use a coordinate proof to prove the Triangle Midsegment Theorem. Coordinate Proof of the Triangle Midsegment Theorem Step 1: Plot 3 points on the coordinate grid. Label them A, B, & C. Connect the points to form ABC. A(6,6), B(4,-6) & C(-8,2) Coordinate Proof of the Triangle Midsegment Theorem Step 2: Algebraically determine the midpoint of sides AB and BC. Then plot those points. Label them D & E. Midpoint: x1+x2 y1+y2 2 , 2 Midpoint AB: 6+4 6+-6 2 , 2 D(5,0) & E(-2,-2) Coordinate Proof of the Triangle Midsegment Theorem Step 3: Calculate the slopes of AC & DE. rise Slope = run mAC = 2/7 mDE = 2/7 Coordinate Proof of the Triangle Midsegment Theorem Step 4: Calculate the lengths of AC & DE. d = (x2 – x1)2 + (y2 – y1) 2 AC = 212 = 253 DE = 53 Applying theTriangle Midsegment Theorem A E D B AB = 10 and CD = 18. Find EB, BC, and AC. C Applying theTriangle Midsegment Theorem X 65 Y Find mVUZ. U V Z Applying theTriangle Midsegment Theorem Find AD, BC, and DC. A x + 50 E x D x + 85 3x + 46 B C Applying theTriangle Midsegment Theorem A B F 70 C 140 E BE AD Find mABC, mD, mA & D mCBE. H OMEWORK Pg. 246: 1-36