6.4 Rectangles

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

Vocabulary Rectangle: a parallelogram with four right angles **Remember a parallelogram has: Opposite sides parallel and congruent Opposite angles congruent Consecutive angles supplementary Diagonals bisect each other

Vocabulary Theorem 6.13: Diagonals of a Rectangle #1 If a parallelogram is a rectangle, then its diagonals are congruent.

Vocabulary Theorem 6.14: Diagonals of a Rectangle #2 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. **(Converse of Theorem 6.13)

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. Answer: KM = 13 feet

Example 1 Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ. Use Properties of Rectangles Answer: GJ= 7.5 feet

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 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. **Parallelogram then Rectangle