# Properties of a Parm

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## Parallelograms

Definition: Quadrilaterals with both pairs of opposite sides parallel.

In any parallelogram:

• The opposite sides are equal and parallel
• The opposite angles are equal
• The diagonals bisect each other (square and rectangle diagonals are the same length)
• One pair of opposite sides are equal and parallel
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## Properties of a Rectangle

Definition: Parallelogram with one 90 degree angle.

• 2 pairs of opposite sides are equal and parallel
• All 4 angles are 90 degrees
• Diagonals are the same length
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## Properties of a Rhombus

Definition: Parallelogram with one pair of adjacent sides equal.

• 2 pairs of parallel sides
• 1 pair of equal sides that are adjacent
• Diagonals are bisected purpendicular
• Diagonals bisect angles

Keep in mind: Pythag can be used because of right angle in triangle and all 4 triangles are congruent.

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## Properties of a Square

Characteristics of a rectangle:

• Diagonals are the same length
• The angles are all 90 degrees

Characteristics of a rhombus:

• 1 Pair of adjacent sides are equal
• Diagonals are bisected purpendicularly
• Diagonals bisect angles (each angle 45 degrees)
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## Properties of a Kite

• Opposite adjacent sides are equal
• Diagonals bisect angles (length wise and the same length)
• Diagonals make 4 right angles at the intersection (not arrowhead)

Remember a kite can take the form of an arrowhead.

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## Properties of a Trapezium

• One pair of opposite sides are parallel

In a isosceles trapizium

• One pair of opposite sides are parallel
• Vertical sides are equal
• Angles on the bottom are equal and angles on the top are equal
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