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.

• 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

Theorem 6.13: Diagonals of a Rectangle #1

If a parallelogram is a rectangle, then its diagonals are congruent.

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)

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

Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ.

Use Properties of Rectangles

Answer: GJ= 7.5 feet

Use Properties of Rectangles and Algebra

Quadrilateral RSTU is a rectangle. If mRTU = 8x + 4 and mSUR = 3x – 2, find x.

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