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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

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**Rhombus Parallelogram with 4 congruent sides**

* all properties of parallelograms * Diagonals are * Diagonals Bisect each pair of opposite angles

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**Rectangle A parallelogram with 4 right angles**

* All properties of Parallelograms *Diagonals are congruent

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**SQUARE A parallelogram with 4 right angles and 4 congruent sides**

*All properties of parallelograms *All properties of Rhombuses *All properties of Rectangles SQUARE

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**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

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**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

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**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

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**Example: ABCD is a rhombus.**

Find the value of x 140 x A B C D <B and <C are suppl. X = 40

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**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

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**Example: GHJK is a parallelogram**

8 6 L 8 Find A. JH =_______ B. LH = ______ 6

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**Example: in Parallelogram ABCD, m<C=105**

Find: A. m<A =____ B. m<D = _____ 75 105

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**Example: WXYZ is a parallelogram, find x**

4x-9=3x+18 -3x -3x X-9=18 +9 +9 X=27

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**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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Geometry SECTION 6: QUADRILATERALS. Properties of Parallelograms.

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