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

A kite is a quadrilateral.

  • Opposite adjacent sides are equal
  • Adjacent angles 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

A trapezium is a quadrilateral.

  • 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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