Chapter 6.4 and 6.5

Rectangles, Squares, and Rhombi

RectangleO A rectangle is a parallelogram with

four right angles.

Concept 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.

A. 3 feet

B. 7.5 feet

C. 9 feet

D. 12 feet

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

Use Properties of Rectangles and Algebra

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

A. x = 1

B. x = 3

C. x = 5

D. x = 10

Quadrilateral EFGH is a rectangle. If mFGE = 6x – 5 and mHFE = 4x – 5, find x.

Concept 2

Matt is building a swimming pool in his backyard. He measures the length and width of the pool so that opposite sides are parallel. He also measures the diagonals of the pool to make sure that they are congruent. How does he know that the measure of each corner is 90?

A. Since opp. sides are ||, STUR must be a rectangle.

B. Since opp. sides are , STUR must be a rectangle.

C. Since diagonals of the are , STUR must be a rectangle.

D. STUR is not a rectangle.

Rectangles and Coordinate Geometry

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.Step 1 Use the Distance

Formula to determine

whether JKLM is a parallelogram bydetermining if

opposite sides are congruent.

A. yes

B. no

C. cannot be determined

Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1). Determine whether WXYZ is a rectangle by using the Distance Formula.

RhombusO A rhombus is a parallelogram with all

four sides congruent.

Concept 1

Use Properties of a Rhombus

A. The diagonals of rhombus WXYZ intersect at V.If mWZX = 39.5, find mZYX.

Use Properties of a Rhombus

B. ALGEBRA The diagonals of rhombus WXYZ intersect at V. If WX = 8x – 5 and WZ = 6x + 3, find x.

A. mCDB = 126

B. mCDB = 63

C. mCDB = 54

D. mCDB = 27

A. ABCD is a rhombus. Find mCDB if mABC = 126.

A. x = 1

B. x = 3

C. x = 4

D. x = 6

B. ABCD is a rhombus. If BC = 4x – 5 and CD = 2x + 7, find x.

SquareO A square is a parallelogram with four

congruent sides and four right angles.

Concept 3

Concept

Use Conditions for Rhombi and Squares

GARDENING Victor is measuring the boundary of a new garden. He wants the garden to be square. He has set each of the corner stakes 6 feet apart. What does Victor need to know to make sure that the garden is square?

A. The diagonal bisects a pair of opposite angles.

B. The diagonals bisect each other.

C. The diagonals are perpendicular.

D. The diagonals are congruent.

Ariel has a shape he knows to be a parallelogram and all four sides are congruent. Which information does he need to know to determine whether it is also a square?

Classify Quadrilaterals Using Coordinate GeometryDetermine whether parallelogram ABCD is

a rhombus, a rectangle, or a square for A(–2, –1), B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain.

A. rhombus only

B. rectangle only

C. rhombus, rectangle, and square

D. none of these

Determine whether parallelogram EFGH is a rhombus, a rectangle, or a square for E(0, –2), F(–3, 0), G(–1, 3), and H(2, 1). List all that apply.