![]() ![]() If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle by Theorem 6-14. From Lesson 6-6, you know that XYZW is a parallelogram. 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. The quadrilateral XYZW formed by connecting the midpoints of ABCD is shown below. The y-coordinates of all points on a horizontal line are the same, so points R and A have the same y-coordinates. Explain why you can assign the same y-coordinate to points R and A. ![]() Proofs Using Coordinate Geometry Lesson 6-7 Additional Examples Examine trapezoid TRAP. Because TP lies on the horizontal x-axis, RA also must be horizontal. In a trapezoid, only one pair of sides is parallel. Placing Figures in the Coordinate Plane Lesson 6-7 Notes 6-7 Placing Figures in the Coordinate Plane Lesson 6-7 Notes The midsegment of a trapezoid is the segment that joins the midpoints of the nonparallel opposite sides. AD in Exercise 3 midpoint: (a, 0) slope: undefined 6-7 parallelogram M (b, c + a) M(2a, 0), D(a, –b) A(0, b), D(a, 0) Find the coordinates of the midpoint and the slope. Proofs Using Coordinate Geometry Lesson 6-7 Check Skills You’ll Need Solutions (continued) 6-7ī a – b 2 c + a 2 b 2 a 2 midpoint:, slope: midpoint:, slope: c + a b Placing Figures in the Coordinate Plane Lesson 6-6 Lesson Quiz Find the missing coordinates of each figure. Since BOAO the coordinates of B are (–a, 0). Also, since (–2) = –1, adjacent sides are perpendicular to one another. Since the slopes of opposite sides are equal, opposite sides are parallel. The slope () of the two longer segments is, or, and the slope of the two shorter segments is, or –2. The coordinates of the midpoints are (, 2), (, 0), (, –2), and (, 0). Proofs Using Coordinate Geometry Lesson 6-7 Check Skills You’ll Need Solutions 1. ![]() isosceles triangle Check Skills You’ll Need 6-7 What do you notice about the quadrilateral? Give the coordinates of B without using any new variables. Then, connect the midpoints of consecutive sides to form a quadrilateral. Proofs Using Coordinate Geometry Lesson 6-7 Check Skills You’ll Need (For help, go to Lesson 6-6.) 1. ![]()
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