1. Bell Ringer

2. Rhombus, Rectangles, and Squares

3. Rhombus- is a parallelogram with four congruent sides.
Rectangle – is a parallelogram with four right angles
Square – is a parallelogram with four congruent sides and four right angles

4. In the diagram, ABCD is a rectangle.
Example 1
Use Properties of Special Parallelograms
In the diagram, ABCD is a rectangle.
Find AD and AB. a. b.
Find mA, mB, mC, and mD.
SOLUTION
By definition, a rectangle is a parallelogram, so ABCD is a parallelogram. Because opposite sides of a parallelogram are congruent, AD = BC = 5 and AB = DC = 8. a.
By definition, a rectangle has four right angles, so mA = mB = mC = mD = 90°. b. 4

5. Now You Try  In the diagram, PQRS is a rhombus. Find QR, RS, and SP.
Use Properties of Special Parallelograms
In the diagram, PQRS is a rhombus.
Find QR, RS, and SP. 1.
ANSWER
QR = 6, RS = 6, SP = 6 5

6. Use the information in the diagram to name the special quadrilateral.
Example 2
Identify Special Quadrilaterals
Use the information in the diagram to name the special quadrilateral.
SOLUTION
Because all of the sides are not the same length, you know that the quadrilateral is not a square.
The quadrilateral has four right angles. So, by the Rectangle Corollary, the quadrilateral is a rectangle. 6

7. Now You Try 
Identify Special Quadrilaterals
Use the information in the diagram to name the special quadrilateral. 2.
ANSWER
rhombus 3.
ANSWER
square 7

8. ABCD is a rhombus. Find the value of x.
Example 3
Use Diagonals of a Rhombus
ABCD is a rhombus. Find the value of x.
SOLUTION
By Theorem 6.10, the diagonals of a rhombus are perpendicular. Therefore, BEC is a right angle, so ∆BEC is a right triangle.
By the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. So, x = 90 – 60 = 30. 8

9. The diagonals measure 7 ft 4 in. and
Example 4
Use Diagonals of a Rectangle
You nail four pieces of wood together to build a four-sided frame, as shown. What is the shape of the frame? a.
The diagonals measure 7 ft 4 in. and
7 ft 2 in. Is the frame a rectangle? b.
SOLUTION
The frame is a parallelogram because both pairs of opposite sides are congruent. a. b.
The frame is not a rectangle because the diagonals are not congruent. 9

10. Now You Try  Find the value of x. rhombus ABCD 4. ANSWER 90
Use Diagonals
Find the value of x.
rhombus ABCD 4.
ANSWER 90
rectangle EFGH 5.
ANSWER 12
square JKLM 6.
ANSWER 45 10

11. Now You Try 

12. Now You Try 

13. Now You Try 

14. Now You Try 

15. Now You Try 

16. Now You Try 
19. A B
ABCD is a square find x 5x D C

17. Page 328

18. Complete Pages 328-330 #s 8-30 Even only