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Then/Now You used properties of parallelograms and determined whether quadrilaterals were parallelograms. Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles.

Concept 1

Example 1 Use Properties of Rectangles CONSTRUCTION A rectangular garden gate is reinforced with diagonal braces to prevent it from sagging. If JK = 12 feet, and LN = 6.5 feet, find KM.

Example 1 A.3 feet B.7.5 feet C.9 feet D.12 feet Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ.

Example 2 Use Properties of Rectangles and Algebra Quadrilateral RSTU is a rectangle. If m  RTU = 8x + 4 and m  SUR = 3x – 2, find x.

Example 2 A.x = 1 B.x = 3 C.x = 5 D.x = 10 Quadrilateral EFGH is a rectangle. If m  FGE = 6x – 5 and m  HFE = 4x – 5, find x.

Concept 2

Example 3 Proving Rectangle Relationships ART Some artists stretch their own canvas over wooden frames. This allows them to customize the size of a canvas. In order to ensure that the frame is rectangular before stretching the canvas, an artist measures the sides and the diagonals of the frame. If AB = 12 inches, BC = 35 inches, CD = 12 inches, DA = 35 inches, BD = 37 inches, and AC = 37 inches, explain how an artist can be sure that the frame is rectangular.

Example 4 Rectangles and Coordinate Geometry Quadrilateral JKLM has vertices J(–2, 3), K(1, 4), L(3, –2), and M(0, –3). Determine whether JKLM is a rectangle using the Distance Formula.

Example 4 Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1). What are the lengths of diagonals WY and XZ? A. B.4 C.5 D.25

Homework: Pg. 426 #’s 2, 4, 6, 8, & 9