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Examine trapezoid TRAP . Explain why you can assign the same y -coordinate to points R and A .

In a trapezoid, only one pair of sides is parallel. In TRAP , TP || RA . Because TP lies on the horizontal x -axis, RA also must be horizontal. . Proofs Using Coordinate Geometry. LESSON 6-7. Additional Examples.

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Examine trapezoid TRAP . Explain why you can assign the same y -coordinate to points R and A .

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  1. In a trapezoid, only one pair of sides is parallel. In TRAP, TP || RA . Because TP lies on the horizontal x-axis, RA also must be horizontal. Proofs Using Coordinate Geometry LESSON 6-7 Additional Examples Examine trapezoid TRAP. Explain why you can assign the same y-coordinate to points R and A. The y-coordinates of all points on a horizontal line are the same, so points R and A have the same y-coordinates. Quick Check

  2. The quadrilateral XYZW formed by connecting the midpoints of ABCD is shown below. Proofs Using Coordinate Geometry LESSON 6-7 Additional Examples Use coordinate geometry to prove that the quadrilateral formed by connecting the midpoints of rhombus ABCD is a rectangle. From Lesson 6-6, you know that XYZW is a parallelogram. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle by Theorem 6-14.

  3. ( –2a)2 + (2b)2 = 4a2 + 4b2 XZ = (–a – a)2 + (b – (–b))2 = ( –2a)2 + (–2b)2 = 4a2 + 4b2 YW = (–a – a)2 + (– b – b)2 = Proofs Using Coordinate Geometry LESSON 6-7 Additional Examples Quick Check (continued) To show that XYZW is a rectangle, find the lengths of its diagonals, and then compare them to show that they are equal. Because the diagonals are congruent, parallelogram XYZW is a rectangle.

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