Section 6 4 Notes Rectangles EQ What are

Parallelogram Review • How do I know that a quadrilateral is a parallelogram?

Vocab! - a parallelogram with four right angles. A rectangle has the following properties:

Example 1 A rectangular garden gate is reinforced with diagonal braces to prevent it

Example 2 Quadrilateral RSTU is a rectangle. If m∠RTU = (8 x + 4)

You Try! 1. Quadrilateral EFGH is a rectangle. If GH = 6 feet and

Converse of Diagonals of a Rectangle - If the diagonals are congruent, then the

Example 3 In rectangle QRST, QS= 5 x – 31 and RT = 2

How to prove a rectangle with coordinate geometry? 1. Show that opposite sides are

Example 4 Quadrilateral JKLM has vertices J(– 2, 3), K(1, 4), L(3, – 2),

You Try! Graph the quadrilateral with the given vertices. Determine whether the figure is

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Section 6. 4 Notes: Rectangles EQ: What are the properties of the diagonals of a rectangle?

Parallelogram Review • How do I know that a quadrilateral is a parallelogram?

Vocab! - a parallelogram with four right angles. A rectangle has the following properties: Rectangle All four angles are right angles. Opposite sides are parallel and congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. Parallelogram properties - If a parallelogram is a rectangle, then its diagonals are Diagonals of congruent. a Rectangle

Example 1 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 2 Quadrilateral RSTU is a rectangle. If m∠RTU = (8 x + 4) and m∠SUR = (3 x – 2) , solve for x.

You Try! 1. Quadrilateral EFGH is a rectangle. If GH = 6 feet and FH = 15 feet, find GJ. 2. Quadrilateral EFGH is a rectangle. If m∠FGE = (6 x – 5) and m∠HFE = (4 x – 5) , solve for x.

Converse of Diagonals of a Rectangle - If the diagonals are congruent, then the parallelogram is a rectangle.

Example 3 In rectangle QRST, QS= 5 x – 31 and RT = 2 x + 11. Find the lengths of the diagonals of QRST.

How to prove a rectangle with coordinate geometry? 1. Show that opposite sides are congruent (or parallel). 2. Show that diagonals are congruent.

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. *(Pythagorean Theorem is also acceptable) (and recommended)

You Try! Graph the quadrilateral with the given vertices. Determine whether the figure is a rectangle. Justify your answer using the indicated formula. A(– 3, 1), B(– 3, 3), C(3, 3), D(3, 1)