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## Notes 8-4, 8-5

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**Notes 8-4, 8-5**Rectangles, Rhombi, and Squares**What is a Rectangle?**A rectangleis a quadrilateral with four right angles.**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)**What is a Rhombus?**A rhombusis a quadrilateral with four congruent sides.**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**What is a Square?**A square is a quadrilateral with four right angles and four congruent sides. A square is a parallelogram, a rectangle, and a rhombus.**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.TR2.CE 35 ft 29 ft**Lesson Quiz: Part II**PQRS is a rhombus. Find each measure. 3.QP4. mQRP 42 51°