Notes 8-4, 8-5Rectangles, Rhombi, and

Squares

A rectangle is a quadrilateral with four right angles.

What is a Rectangle?

Since a rectangle is a parallelogram, a rectangle “inherits” all the properties of parallelograms.

Example:

A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM.

Example:

Carpentry The rectangular gate has diagonal braces. Find HJ.

HJ = GK = 48

Find HK.

JG = 2JL = 2(30.8) = 61.6

Proving a Quadrilateral is a Rectangle in the Coordinate Plane:

• Prove Definition:– Use slopes to prove opposite sides ║

(parallelogram), and consecutive sides are perpendicular (rectangle).

• Prove Diagonals are congruent:– Use distance formula to prove opposite

sides congruent (parallelogram), and then prove diagonals are congruent (rectangle)

A rhombus is a quadrilateral with four congruent sides.

What is a Rhombus?

Example:

TVWX is a rhombus. Find TV.

TV = 3(1.3) + 4 = 7.9

Example:

TVWX is a rhombus. Find mVTZ.

mVTZ = [5(5) – 5)]° = 20°

Example:

CDFG is a rhombus. Find CD.

CD = 42.5

Find mGCH if mGCD = (b + 3)°and mCDF = (6b – 40)°

mGCH = 17°

Example:

Find the area of the rhombii

A = ½(12)(26) = 156 Sq. Units A = ½(14)(10) = 70 Sq. Units

Example:

Find the area of the rhombus

A = 1080 m2

A square is a quadrilateral with four right angles and four congruent sides.

A square is a parallelogram, a rectangle, and a rhombus.

What is a Square?

To Prove a Parallelogram is a Rectangle, Rhombus or a

Square:• Use distance formula to show

diagonals are congruent (rectangle).• Use slopes to prove consecutive

sides are perpendicular (rectangle).• Use slopes to prove diagonals are

perpendicular (rhombus).• If figure is both a rectangle and

rhombus, then it is a square.

Lesson Quiz: Part I

A slab of concrete is poured with diagonal spacers. In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length.

1. TR 2. CE

35 ft 29 ft

Lesson Quiz: Part II

PQRS is a rhombus. Find each measure.

3. QP 4. mQRP

42 51°