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Parallelogram Properties Worksheets

Use consecutive angles, opposite sides, bisected diagonals and diagonal-split angles in direct or algebra practice.

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Use the parallelogram properties to find each requested measure. In algebra mode, solve for x and report the measure.

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Use only guaranteed parallelogram facts

Opposite sides are equal, consecutive angles are supplementary, and the diagonals bisect each other.

Learning objective

What this activity builds

Apply parallelogram relationships to find missing lengths, angles and linear-equation solutions.

Worked example

A parallelogram has one interior angle of 112 degrees. A diagonal splits its adjacent interior angle into 25 degrees and an unknown angle. Find the unknown.

43 degrees.

The adjacent interior angle is 180 - 112 = 68 degrees. The remaining part is 68 - 25 = 43 degrees.

Teaching notes

Make the practice count

  • Opposite sides are equal and consecutive interior angles are supplementary.
  • Diagonals bisect each other; one half is half the whole diagonal.
  • An arbitrary parallelogram diagonal does not necessarily bisect its vertex angle.

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Eight diagrams include two questions each for consecutive angles, opposite sides, diagonal half/whole lengths and a diagonal-split angle. Algebra mode asks for both x and the indicated measure.

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Math SheetNameScoreTeacherDateProperties of ParallelogramsUse opposite sides, supplementary consecutive angles, bisected diagonals, and the marked diagonal split to find each measure.1. angle ABC = 84 deg. Find angle DAB.ABCDangle DAB =2. CD = 58 units. Find AB.ABCDAB =3. angle ABC = 110 deg; angle BAC = 28 deg. Find angle CAD.ABCDangle CAD =4. angle ABC = 89 deg; angle BAC = 40 deg. Find angle CAD.ABCDangle CAD =Opposite sides are equal, consecutive angles are supplementary, and diagonals bisect each other.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateProperties of ParallelogramsUse opposite sides, supplementary consecutive angles, bisected diagonals, and the marked diagonal split to find each measure.5. AC = 44 units. Find AO.ABCDOAO =6. angle ABC = 71 deg. Find angle DAB.ABCDangle DAB =7. CD = 7 units. Find AB.ABCDAB =8. AO = 12 units. Find AC.ABCDOAC =Opposite sides are equal, consecutive angles are supplementary, and diagonals bisect each other.math-sheet.comPage 2 of 2

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