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

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

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

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

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

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

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

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

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 C D 7x-12 2x+13 7x-12 = 2x+13 5x-12=13 5x=25 x=5

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

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

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

Example: UVWX is a parallelogram
Z 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

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