1 / 18

Notes 8-4, 8-5

Notes 8-4, 8-5. Rectangles, Rhombi, and Squares. What is a Rectangle?. A rectangle is a quadrilateral with four right angles. Since a rectangle is a parallelogram, a rectangle “inherits” all the properties of parallelograms. Example:.

haynesp
Download Presentation

Notes 8-4, 8-5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Notes 8-4, 8-5 Rectangles, Rhombi, and Squares

  2. What is a Rectangle? A rectangleis a quadrilateral with four right angles.

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

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

  5. Example: Carpentry The rectangular gate has diagonal braces. Find HJ. HJ = GK = 48 Find HK. JG = 2JL = 2(30.8) = 61.6

  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)

  7. What is a Rhombus? A rhombusis a quadrilateral with four congruent sides.

  8. Example: TVWX is a rhombus. Find TV. TV =3(1.3)+ 4 = 7.9

  9. Example: TVWX is a rhombus. Find mVTZ. mVTZ =[5(5) – 5)]° = 20°

  10. Example: CDFG is a rhombus. Find CD. CD = 42.5 Find mGCH if mGCD = (b + 3)° and mCDF = (6b – 40)° mGCH = 17°

  11. Example: Find the area of the rhombii A = ½(12)(26) = 156 Sq. Units A = ½(14)(10) = 70 Sq. Units

  12. Example: Find the area of the rhombus A = 1080 m2

  13. 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.

  14. 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.

  15. 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

  16. Lesson Quiz: Part II PQRS is a rhombus. Find each measure. 3.QP4. mQRP 42 51°

More Related