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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°