Properties to find Measures Angles Sides etc parallelogram

• Parallelogram

  • Opposite sides are congruent
  • Opposite sides are parallel
• Finding measures of angles, sides, and other quantities in a parallelogram

  1. Draw the given figure

  2. Identify opposite sides and angles

  3. Apply properties of parallelograms

  4. Formulate and solve equations
• Congruent

  Equal in measure
• Supplementary angles

  The sum of the measures is 180 degrees
• Parallelogram properties

  • Opposite sides are congruent
  • Opposite angles are congruent
  • Consecutive angles are supplementary
• Solving for x to make a quadrilateral a parallelogram

  1. Draw the given figure

  2. Identify opposite sides

  3. Set up equation using congruent opposite sides

  4. Solve for x

  5. Substitute x to find side lengths
• Finding angle measures in a parallelogram

  1. Draw the given figure

  2. Identify opposite angles

  3. Use congruent opposite angles property

  4. Use supplementary consecutive angles property

  5. Solve for unknown angle measures
• Draw and mark the given parallelogram

  1. Draw parallelogram PQRS

  2. Mark angles P and Q
• Angle P

  23x + 5
• Angle Q

  13x - 5
• Consecutive angles in a parallelogram are supplementary
• Formulate an equation and solve


  1. 23x + 5 + 13x - 5 = 180

  2. Combine like terms: 36x = 180

  3. Divide both sides by 36: x = 5
• Angle P = 23(5) + 5 = 120 degrees
• Angle Q = 13(5) - 5 = 60 degrees
• The sum of angles P and Q is 180 degrees
• Parallelogram LOVE


  Angle O = y<|>Angle E = 86 degrees<|>Angle VLO = 30 degrees<|>Angle EDL = 2x
• Solve for y, z, x

  1. y = 86 degrees

  2. z = 64 degrees

  3. 2x = 30, so x = 15
• Angle L = 64 degrees
• Angles L and O have a ratio of 3:7
• Solve for the measures of angles L and O

  1. 3x + 7x = 180, so x = 18

  2. Angle L = 3(18) = 54 degrees

  3. Angle O = 7(18) = 126 degrees
• Solve for the lengths of segments when diagonals bisect

  1. SE = 12 dm, so SU = 24 dm

  2. SE = EU, so EU = 12 dm
• Solve for the variable to make a quadrilateral a parallelogram

  1. 3x - 7 = 2x, so x = 7

  2. 5y - 3 = 2y + 9, so y = 4
• Area of a parallelogram

  Area = base x height
• Perimeter of a parallelogram

  Perimeter = 2 x (length + width)
• Parallelogram PQRS

  • Area = 60 square cm
  • Perimeter = 32 cm