1. Parallelogram
A quadrilateral with both pairs of opposite sides parallel
*opposite sides are congruent
*opposite angles are congruent
*diagonals bisect each other

2. Rhombus Parallelogram with 4 congruent sides
* all properties of parallelograms
* Diagonals are 
* Diagonals Bisect each pair of opposite angles

3. Rectangle A parallelogram with 4 right angles
* All properties of Parallelograms
*Diagonals are congruent

4. SQUARE A parallelogram with 4 right angles and 4 congruent sides
*All properties of parallelograms
*All properties of Rhombuses
*All properties of Rectangles
SQUARE

5. How do they fit together?
Parallelogram
Rhombus
Rectangle
When comparing top down, the shapes are sometimes. When comparing bottom up, the shapes are always
Square

6. Example: decide if the statement is always, sometimes or never true.
1. A rectangle is a square
1. Sometimes
2. Always
3. Always
4. Always
5. Sometimes
6. Never
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

7. Example: ABCD is a rectangle.
m<B= 8x+26. What is the value of x B C D A
8x+26
90 = 8x+26
64 = 8x
8 = x

8. Example: ABCD is a rhombus.
Find the value of x
140 x A B C D
<B and <C are suppl.
X = 40

9. Example: ABCD is a rectangle.
Find the value of x A B C D
7x-12
2x+13
7x-12 = 2x+13
5x-12=13
5x=25
x=5

10. Example: GHJK is a parallelogram8 6 L 8
Find A. JH =_______
B. LH = ______ 6

11. Example: in Parallelogram ABCD, m<C=105
Find: A. m<A =____
B. m<D = _____ 75
105

12. Example: WXYZ is a parallelogram, find x
4x-9=3x+18
-3x -3x
X-9=18
+9 +9
X=27

13. Example: UVWX is a parallelogramZ 14
#3. The angles are supplementary
55+7x-8 = 180
7x+47 = 180
7x = 133
x= 19
1. XU = 15, UW = 28, WZ= _____ 60
2. <VWX = 120, find m<WXU = ___
3. m<UVW = 55, m<VWX=7x-8, find x

14. Today's Work