1. 6.4 Notes
Rectangles

2. Properties of Rectangles
A rectangle is a parallelogram with four right angles. By definition, a rectangle has the following properties.
All four angles are right angles.
Opposite sides are parallel and congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.

3. The Diagonals of a Rectangle

4. Example 1
a) 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.

5. Example 1
B) Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ.

6. Example 2
a) Quadrilateral RSTU is a rectangle. If mÐRTU = (8x + 4) and mÐSUR = (3x – 2), solve for x.

7. Example 2
B) Quadrilateral EFGH is a rectangle. If mÐFGE = (6x – 5) and mÐHFE = (4x –5), solve for x.

8. The Converse is also true…

9. Example 3
Some artists stretch their own canvas over wooden frames. This allows them to customize the size of 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.

10. Example 4
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.

11. Enrichment
Since I figured you would all be bored with rectangles (since you’ve been using rectangles since kindergarten) you may work with your partner or a group or as a class to work on this enrichment worksheet. I will show the answers at the end of class but I will also be collecting it!