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6.4 Rectangles

6.4 Rectangles. You used properties of parallelograms and determined whether quadrilaterals were parallelograms. Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. Then/Now. Rectangle: a parallelogram with four right angles.

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6.4 Rectangles

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  1. 6.4 Rectangles

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

  3. 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

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

  5. 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) Vocabulary

  6. 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

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

  8. 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

  9. 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 Example 3

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