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Chapter 6: Quadrilaterals

Chapter 6: Quadrilaterals. 6.7 Proofs Using Coordinate Geometry. Trapezoid Midsegment Theorem: (1) the midsegment of a trapezoid is parallel to the bases (2) the length of the midsegment of a trapezoid is half the sum of the lengths of the bases. Example 1.

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Chapter 6: Quadrilaterals

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  1. Chapter 6: Quadrilaterals 6.7 Proofs Using Coordinate Geometry

  2. Trapezoid Midsegment Theorem: • (1) the midsegment of a trapezoid is parallel to the bases • (2) the length of the midsegment of a trapezoid is half the sum of the lengths of the bases

  3. Example 1 • Write a coordinate proof of the Trapezoid Midsegment Theorem. • Given: MN is the midsegment of trapezoid TRAP • Prove: MN || TP, MN || RA, and MN = ½ (TP + RA)

  4. Example 2 • Given: MNPO is a rectangle; T,W,V,U are midpoints of its sides • Prove: TWVU is a rhombus

  5. Example 3 • Given: The vertices of a rectangle are A(0,0), B(0,2b), C(2a,2b), D(2a,0) • Prove: The diagonals bisect each other

  6. Example 4 • Given: Kite DEFG with DE = EF and DG = GF; K,L,M,N are midpoints of the sides. • Prove: KLMN is a rectangle

  7. Homework • p 349: • 2-7 as coordinate proofs (no plan)

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