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Worksheets›Geometry›Polygons & quadrilaterals›Properties of parallelograms

Properties of Parallelograms Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

GeometryCCSS HSG.CO.C.11Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Opposite sides

  1. 1.Find x.ABCD2x + 85x − 19
  2. 2.Find x.ABCD5x − 196x − 25
  3. 3.Find x.ABCD3x + 34x − 2
  4. 4.Find x.ABCD6x − 345x − 25
  5. 5.Find x.ABCDx + 54x − 31
  6. 6.Find x.ABCD2x + 215x − 9
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

In a parallelogram, opposite sides are equal and opposite angles are equal. Angles next to each other (consecutive angles) add to 180°, because the sides between them are parallel. Pick the fact that links the two marked parts, write the equation and solve.

EasyFind x.ABCD4x − 23x + 6Opposite sidesMediumFind x.A(x + 42)°BC(4x)°DOpposite anglesHardFind x.A(4x + 14)°B(6x + 36)°CDConsecutive angles

How to solve it: a worked example

ABCD is a parallelogram. Find the value of x.

  1. StartFind x.ABCD6x − 283x + 2
  2. Opposite sides are equal(6x − 28) = (3x + 2)
  3. Collect the x-terms on one side3x = 30
  4. Solve for xx = 10
  5. Answerx = 10

Common mistakes to watch for

  • Setting consecutive angles equal instead of adding them to 180°.
  • Adding opposite angles to 180° instead of setting them equal.
  • Pairing a side with the side next to it instead of the opposite side.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Interior and exterior angles of polygonsArea of regular polygonsAngle pair equationsParallel lines and transversalsTriangle angle sum and exterior angles

FAQ

Which parts of a parallelogram are equal?

Opposite sides are equal, opposite angles are equal, and the diagonals bisect each other. Consecutive angles add to 180°.

Are the diagonals of a parallelogram equal?

Not in general. They are equal only in a rectangle (including a square).

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix properties of parallelograms with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.