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Midsegments of Triangles

Midsegments of Triangles. Honors Geometry. Vocabulary. Midsegment of a triangle – a segment connecting the midpoints of two sides of the triangle. Midsegment Investigation. Geogebra Exploration. Theorem.

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Midsegments of Triangles

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  1. Midsegments of Triangles Honors Geometry

  2. Vocabulary Midsegment of a triangle – a segment connecting the midpoints of two sides of the triangle.

  3. Midsegment Investigation Geogebra Exploration

  4. 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.

  5. Vocabulary Coordinate Proof – Using coordinate geometry and algebra to prove a hypothesis. We can use a coordinate proof to prove the Triangle Midsegment Theorem.

  6. 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)

  7. 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)

  8. Coordinate Proof of the Triangle Midsegment Theorem Step 3: Calculate the slopes of AC & DE. rise run mAC = 2/7 mDE = 2/7 Slope =

  9. Coordinate Proof of the Triangle Midsegment Theorem Step 4: Calculate the lengths of AC & DE. d =  (x2 – x1)2 + (y2 – y1) 2 AC = 212 = 253 DE = 53

  10. Applying theTriangleMidsegment Theorem AB = 10 and CD = 18. Find EB, BC, and AC. A E B D C

  11. Applying theTriangleMidsegment Theorem X Find mVUZ. 65 U Z Y V

  12. Applying theTriangleMidsegment Theorem Find AD, BC, and DC. A x + 50 E B x + 85 x D C 3x + 46

  13. Applying theTriangleMidsegment Theorem BE AD Find mABC, mD, mA & mCBE. A B C 140 70 F D E

  14. Homework Pg. 246: 1-36

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