Worksheets · Geometry

Properties of parallelograms worksheet

Four facts do all the work: opposite sides are equal, opposite angles are equal, consecutive angles add to 180, and the diagonals cut each other in half. Each one turns a picture into an equation.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of Parallelograms

Date Period

Find x in each parallelogram.

  1. Find x7x + 39°6x - 28°ABCD
  2. In parallelogram ABCD, AB=7x+6 and CD=6x+21. Find x
  3. The diagonals of a parallelogram bisect: AE=6x6 and EC=7x+215. Find x
  4. Find x6x + 3°-6x + 207°ABCD
  5. In parallelogram ABCD, AB=8x+4 and CD=6x+200. Find x
  6. The diagonals of a parallelogram bisect: AE=8x+9 and EC=6x+261. Find x
  7. Find x8x + 4°6x + 40°ABCD
  8. In parallelogram ABCD, AB=6x2 and CD=6x+154. Find x
  9. The diagonals of a parallelogram bisect: AE=7x+9 and EC=8x+249. Find x
  10. Find x6x - 11°-6x + 145°ABCD
  11. In parallelogram ABCD, AB=6x7 and CD=7x24. Find x
  12. The diagonals of a parallelogram bisect: AE=8x8 and EC=6x+20. Find x
  13. Find x8x - 10°6x + 26°ABCD
  14. In parallelogram ABCD, AB=6x+3 and CD=8x27. Find x
  15. The diagonals of a parallelogram bisect: AE=7x+7 and EC=7x+203. Find x
  16. Find x7x - 12°-7x + 240°ABCD
  17. In parallelogram ABCD, AB=7x+8 and CD=6x+216. Find x
  18. The diagonals of a parallelogram bisect: AE=6x+12 and EC=8x+250. Find x
  19. Find x6x + 3°-8x + 255°ABCD
  20. In parallelogram ABCD, AB=7x12 and CD=8x28. Find x

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of ParallelogramsAnswer keyVersion 1

Date Period

Find x in each parallelogram.

  1. Find x7x + 39°6x - 28°ABCD13
  2. In parallelogram ABCD, AB=7x+6 and CD=6x+21. Find x15
  3. The diagonals of a parallelogram bisect: AE=6x6 and EC=7x+215. Find x17
  4. Find x6x + 3°-6x + 207°ABCD17
  5. In parallelogram ABCD, AB=8x+4 and CD=6x+200. Find x14
  6. The diagonals of a parallelogram bisect: AE=8x+9 and EC=6x+261. Find x18
  7. Find x8x + 4°6x + 40°ABCD18
  8. In parallelogram ABCD, AB=6x2 and CD=6x+154. Find x13
  9. The diagonals of a parallelogram bisect: AE=7x+9 and EC=8x+249. Find x16
  10. Find x6x - 11°-6x + 145°ABCD13
  11. In parallelogram ABCD, AB=6x7 and CD=7x24. Find x17
  12. The diagonals of a parallelogram bisect: AE=8x8 and EC=6x+20. Find x14
  13. Find x8x - 10°6x + 26°ABCD18
  14. In parallelogram ABCD, AB=6x+3 and CD=8x27. Find x15
  15. The diagonals of a parallelogram bisect: AE=7x+7 and EC=7x+203. Find x14
  16. Find x7x - 12°-7x + 240°ABCD18
  17. In parallelogram ABCD, AB=7x+8 and CD=6x+216. Find x16
  18. The diagonals of a parallelogram bisect: AE=6x+12 and EC=8x+250. Find x17
  19. Find x6x + 3°-8x + 255°ABCD18
  20. In parallelogram ABCD, AB=7x12 and CD=8x28. Find x16

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A=3x+10 and C=5x20

  1. A and C are opposite, so they are equal.
  2. 3x + 10 = 5x - 20.
  3. Solve for x.

The answer is x=15.

Where students go wrong

Setting consecutive angles equal. Opposite angles match; consecutive ones add to 180, and picking the wrong pair gives a plausible answer that is simply not the one.

Also called parallelogram properties, opposite angles or diagonals of a parallelogram.

What you can put on this worksheet

Angles
Find x 8
Sides
In parallelogram ABCD, AB=2x6 and CD=4x+42. Find x 8
Diagonals
The diagonals of a parallelogram bisect: AE=2x6 and EC=4x+42. Find x 8

Questions about these worksheets

Yes. Every properties of parallelograms sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the properties of parallelograms questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: angles, sides and diagonals. Tick as many as you want and set how many of each, or let it spread them evenly.

Setting consecutive angles equal. Opposite angles match; consecutive ones add to 180, and picking the wrong pair gives a plausible answer that is simply not the one.