1. Kites and Rhombi and Squares—Oh My!
Chapter 6-5
Wizard of Oz reference—get it?
Ahh—who asked you anyway!

2. Recognize and apply the properties of rhombi.
Recognize and apply the properties of squares.
rhombus
square
Lesson 5 MI/Vocab

3. Rhombus
Def—A //ogram with 4  sides

4. Properties of a Rhombus
Rhombus  diagonals are  (bisectors)
Rhombus  diagonals bisect pairs of opposite angles
Also has all the properties of a //ogram.
Opposite sides 
Opposite angles 
Consecutive angles supplementary
Diagonals bisect each other

6. The diagonals of a rhombus are perpendicular.
Measures of a Rhombus
A. Use rhombus LMNP to find the value of y if m1 = y2 – 54.
The diagonals of a rhombus are perpendicular.
Answer: The value of y can be 12 or –12.

7. Diagonals bisect opposite angles
Measures of a Rhombus
B. Use rhombus LMNP to find mPNL if mMLP = 64.
32o
64o
64o
Diagonals bisect opposite angles

8. A. Use rhombus ABCD and the given information to find the value of each variable. Find x if m1 = 2x2 – 38.
A. x = 8
B. x = 4 or 12
C. x = 16 or –2
D. x = 8 or –8

9. B. Use rhombus ABCD and the given information to find the value of each variable. Find mCDB if mABC = 126.
A. mCDB = 126
B. mCDB = 63
C. mCDB = 54
D. mCDB = 27

10. Square
Def—A //ogram with 4  sides & 4 Rt. s

11. Properties of a Square
Square has all the properties of a Rectangle and a Rhombus (and a //ogram)

12. //ograms
Rectangles
Rhombi
Squares

13. Explore Plot the vertices on a coordinate plane.
Squares
Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A(–2, –1), B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain.
Explore Plot the vertices on a coordinate plane.
Lesson 5 Ex3

14. Squares
Plan If the diagonals are perpendicular, then ABCD is either a rhombus or a square. The diagonals of a rectangle are congruent. If the diagonals are congruent and perpendicular, then ABCD is a square.
Solve Use the Distance Formula to compare the lengths of the diagonals.
Lesson 5 Ex3

15. Use slope to determine whether the diagonals are perpendicular.
Squares
Use slope to determine whether the diagonals are perpendicular.
Since the slope of is the negative reciprocal of the slope of the diagonals are perpendicular. The lengths of and are the same so the diagonals are congruent. ABCD is a rhombus, a rectangle, and a square.
Lesson 5 Ex3

16. Answer: ABCD is a rhombus, a rectangle, and a square.
Squares
Examine The diagonals are congruent and perpendicular so ABCD must be a square. A square is also a rhombus.
Answer: ABCD is a rhombus, a rectangle, and a square.
Lesson 5 Ex3

17. Kites
Def: A quadrilateral that has two pairs of consecutive congruent sides.

18. Properties of a Kite
If a quadrilateral is a kite then its diagonals are perpendicular.
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

19. Kite

20. Homework
Chapter 6.5
Pg 351
2-5, 6, 15-18, 19, 30-35, 42-44, 48-50

21. Homework
Chapter 6-5
Pg 351
#’s 2-5, 6, 15-18, 19, 30-35, 42-44, 48-50