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

2. What is a Rectangle?
A rectangle is 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 rhombus is a quadrilateral with four congruent sides.

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

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

11. 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°

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

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

15. 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.

16. 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.

17. 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 CE
35 ft
29 ft

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