A quadrilateral with both pairs of opposite sides parallel

*opposite sides are congruent

*opposite angles are congruent

*diagonals bisect each other

Parallelogram with 4 congruent sides

* all properties of parallelograms

* Diagonals are

* Diagonals Bisect each pair of opposite angles

A parallelogram with 4 right angles

* All properties of Parallelograms

*Diagonals are congruent

A parallelogram with 4 right angles and 4 congruent sides

*All properties of parallelograms

*All properties of Rhombuses

*All properties of Rectangles

How do they fit together?Parallelogram

Rhombus Rectangle

Square

When comparing top down, the shapes are sometimes. When comparing bottom up, the shapes are always

Example: decide if the statement is always, sometimes

or never true.

1. A rectangle is a square 1. Sometimes

2. A Square is a rhombus

3. A rhombus is a parallelogram

4. A square is a quadrilateral

5. A parallelogram is a rectangle

6. A square is a trapezoid

2. Always

3. Always

4. Always

5. Sometimes

6. Never

Example: ABCD is a rectangle.

m<B= 8x+26. What is the value of x

90 = 8x+26

64 = 8x

8 = x

B C

DA

8x+26

Example: ABCD is a rhombus.

Find the value of x

140 x

A

B C

D

<B and <C are suppl.

X = 40

Example: ABCD is a rectangle. Find the value of x

A B

CD

7x-12

2x+13

7x-12 = 2x+13

5x-12=13

5x=25

x=5

Example: GHJK is a parallelogram

Find A. JH =_______

B. LH = ______

K J

HG

86

L

8

6

Example: in Parallelogram ABCD, m<C=105

Find: A. m<A =____

B. m<D = _____

A B

CD105

105

75

Example: WXYZ is a parallelogram, find xW

X

Y

Z4x-9

3x+18

4x-9=3x+18

-3x -3x

X-9=18

+9 +9

X=27

Example: UVWX is a parallelogram

U V

WX

Z

1. XU = 15, UW = 28, WZ= _____

2. <VWX = 120, find m<WXU = ___

3. m<UVW = 55, m<VWX=7x-8, find x

#3. The angles are supplementary

55+7x-8 = 180

7x+47 = 180

7x = 133

x= 19

14

60