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.

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Sigma Prep · sigmaprep.io/worksheets Name Properties of Parallelograms Date Period Find each value asked for. Find angles in a parallelogram Find $x$ . Find $x$ . Find $x$ . Find $x$ . Use opposite sides of a parallelogram In parallelogram $A B C D$ , $A B = 7 x - 7$ and $C D = 8 x - 22$ . Find $x$ . In parallelogram $A B C D$ , $A B = 7 x + 6$ and $C D = 8 x - 7$ . Find $x$ . In parallelogram $A B C D$ , $A B = 8 x - 12$ and $C D = - 8 x + 276$ . Find $x$ . In parallelogram $A B C D$ , $A B = 8 x - 10$ and $C D = 6 x + 18$ . Find $x$ . Use the diagonals of a parallelogram The diagonals of a parallelogram bisect: $A E = 10 x - 12$ and $E C = 9 x + 8$ . Find $x$ . The diagonals of a parallelogram bisect: $A E = 10 x + 2$ and $E C = - 9 x + 401$ . Find $x$ . The diagonals of a parallelogram bisect: $A E = 10 x - 9$ and $E C = - 10 x + 431$ . Find $x$ . Find $x$ and $y$ in a parallelogram Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 4 x + 7$ , $C D = 5 x + 2$ , $A D = 5 y + 12$ , $B C = y + 56$ . Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 6 x + 2$ , $C D = 5 x + 12$ , $A D = 6 y - 2$ , $B C = 3 y + 31$ . Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 5 x + 9$ , $C D = 2 x + 30$ , $A D = 2 y + 10$ , $B C = 3 y + 1$ . Find the missing vertex of a parallelogram Three vertices of parallelogram $A B C D$ are $A (- 5, 4)$ , $B (- 3, 4)$ , $C (- 5, 8)$ . Find $D$ . Three vertices of parallelogram $A B C D$ are $A (3, 2)$ , $C (8, 6)$ , $D (6, 7)$ . Find $B$ . Three vertices of parallelogram $A B C D$ are $A (- 1, - 5)$ , $B (2, - 7)$ , $D (0, - 3)$ . Find $C$ . Find sides, angles and diagonals of parallelograms ABCD is a parallelogram. Find $m ∠ A B C$ . ABCD is a parallelogram. Find $A C$ . ABCD is a parallelogram. $A E = 5 x - 52$ and $A C = 3 x - 20$ . Find $A C$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of Parallelograms

Date Period

Find each value asked for.

Find angles in a parallelogram
Find $x$ .
Find $x$ .
Find $x$ .
Find $x$ .

Use opposite sides of a parallelogram
In parallelogram $A B C D$ , $A B = 7 x - 7$ and $C D = 8 x - 22$ . Find $x$ .
In parallelogram $A B C D$ , $A B = 7 x + 6$ and $C D = 8 x - 7$ . Find $x$ .
In parallelogram $A B C D$ , $A B = 8 x - 12$ and $C D = - 8 x + 276$ . Find $x$ .
In parallelogram $A B C D$ , $A B = 8 x - 10$ and $C D = 6 x + 18$ . Find $x$ .

Use the diagonals of a parallelogram
The diagonals of a parallelogram bisect: $A E = 10 x - 12$ and $E C = 9 x + 8$ . Find $x$ .
The diagonals of a parallelogram bisect: $A E = 10 x + 2$ and $E C = - 9 x + 401$ . Find $x$ .
The diagonals of a parallelogram bisect: $A E = 10 x - 9$ and $E C = - 10 x + 431$ . Find $x$ .

Find $x$ and $y$ in a parallelogram
Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 4 x + 7$ , $C D = 5 x + 2$ , $A D = 5 y + 12$ , $B C = y + 56$ .
Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 6 x + 2$ , $C D = 5 x + 12$ , $A D = 6 y - 2$ , $B C = 3 y + 31$ .
Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 5 x + 9$ , $C D = 2 x + 30$ , $A D = 2 y + 10$ , $B C = 3 y + 1$ .

Find the missing vertex of a parallelogram
Three vertices of parallelogram $A B C D$ are $A (- 5, 4)$ , $B (- 3, 4)$ , $C (- 5, 8)$ . Find $D$ .
Three vertices of parallelogram $A B C D$ are $A (3, 2)$ , $C (8, 6)$ , $D (6, 7)$ . Find $B$ .
Three vertices of parallelogram $A B C D$ are $A (- 1, - 5)$ , $B (2, - 7)$ , $D (0, - 3)$ . Find $C$ .

Find sides, angles and diagonals of parallelograms
ABCD is a parallelogram. Find $m ∠ A B C$ .
ABCD is a parallelogram. Find $A C$ .
ABCD is a parallelogram. $A E = 5 x - 52$ and $A C = 3 x - 20$ . Find $A C$ .



Sigma Prep · sigmaprep.io/worksheets Name Properties of ParallelogramsAnswer keyVersion 1 Date Period Find each value asked for. Find angles in a parallelogram Find $x$ . $3$ Find $x$ . $4$ Find $x$ . $11$ Find $x$ . $7$ Use opposite sides of a parallelogram In parallelogram $A B C D$ , $A B = 7 x - 7$ and $C D = 8 x - 22$ . Find $x$ . $15$ In parallelogram $A B C D$ , $A B = 7 x + 6$ and $C D = 8 x - 7$ . Find $x$ . $13$ In parallelogram $A B C D$ , $A B = 8 x - 12$ and $C D = - 8 x + 276$ . Find $x$ . $18$ In parallelogram $A B C D$ , $A B = 8 x - 10$ and $C D = 6 x + 18$ . Find $x$ . $14$ Use the diagonals of a parallelogram The diagonals of a parallelogram bisect: $A E = 10 x - 12$ and $E C = 9 x + 8$ . Find $x$ . $20$ The diagonals of a parallelogram bisect: $A E = 10 x + 2$ and $E C = - 9 x + 401$ . Find $x$ . $21$ The diagonals of a parallelogram bisect: $A E = 10 x - 9$ and $E C = - 10 x + 431$ . Find $x$ . $22$ Find $x$ and $y$ in a parallelogram Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 4 x + 7$ , $C D = 5 x + 2$ , $A D = 5 y + 12$ , $B C = y + 56$ . $x = 5$ , $y = 11$ Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 6 x + 2$ , $C D = 5 x + 12$ , $A D = 6 y - 2$ , $B C = 3 y + 31$ . $x = 10$ , $y = 11$ Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 5 x + 9$ , $C D = 2 x + 30$ , $A D = 2 y + 10$ , $B C = 3 y + 1$ . $x = 7$ , $y = 9$ Find the missing vertex of a parallelogram Three vertices of parallelogram $A B C D$ are $A (- 5, 4)$ , $B (- 3, 4)$ , $C (- 5, 8)$ . Find $D$ . $(- 7, 8)$ Three vertices of parallelogram $A B C D$ are $A (3, 2)$ , $C (8, 6)$ , $D (6, 7)$ . Find $B$ . $(5, 1)$ Three vertices of parallelogram $A B C D$ are $A (- 1, - 5)$ , $B (2, - 7)$ , $D (0, - 3)$ . Find $C$ . $(3, - 5)$ Find sides, angles and diagonals of parallelograms ABCD is a parallelogram. Find $m ∠ A B C$ . $114^{\circ}$ ABCD is a parallelogram. Find $A C$ . $6$ ABCD is a parallelogram. $A E = 5 x - 52$ and $A C = 3 x - 20$ . Find $A C$ . $16$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Properties of ParallelogramsAnswer keyVersion 1

Date Period

Find each value asked for.

Find angles in a parallelogram
Find $x$ . $3$
Find $x$ . $4$
Find $x$ . $11$
Find $x$ . $7$

Use opposite sides of a parallelogram
In parallelogram $A B C D$ , $A B = 7 x - 7$ and $C D = 8 x - 22$ . Find $x$ . $15$
In parallelogram $A B C D$ , $A B = 7 x + 6$ and $C D = 8 x - 7$ . Find $x$ . $13$
In parallelogram $A B C D$ , $A B = 8 x - 12$ and $C D = - 8 x + 276$ . Find $x$ . $18$
In parallelogram $A B C D$ , $A B = 8 x - 10$ and $C D = 6 x + 18$ . Find $x$ . $14$

Use the diagonals of a parallelogram
The diagonals of a parallelogram bisect: $A E = 10 x - 12$ and $E C = 9 x + 8$ . Find $x$ . $20$
The diagonals of a parallelogram bisect: $A E = 10 x + 2$ and $E C = - 9 x + 401$ . Find $x$ . $21$
The diagonals of a parallelogram bisect: $A E = 10 x - 9$ and $E C = - 10 x + 431$ . Find $x$ . $22$

Find $x$ and $y$ in a parallelogram
Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 4 x + 7$ , $C D = 5 x + 2$ , $A D = 5 y + 12$ , $B C = y + 56$ . $x = 5$ , $y = 11$
Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 6 x + 2$ , $C D = 5 x + 12$ , $A D = 6 y - 2$ , $B C = 3 y + 31$ . $x = 10$ , $y = 11$
Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 5 x + 9$ , $C D = 2 x + 30$ , $A D = 2 y + 10$ , $B C = 3 y + 1$ . $x = 7$ , $y = 9$

Find the missing vertex of a parallelogram
Three vertices of parallelogram $A B C D$ are $A (- 5, 4)$ , $B (- 3, 4)$ , $C (- 5, 8)$ . Find $D$ . $(- 7, 8)$
Three vertices of parallelogram $A B C D$ are $A (3, 2)$ , $C (8, 6)$ , $D (6, 7)$ . Find $B$ . $(5, 1)$
Three vertices of parallelogram $A B C D$ are $A (- 1, - 5)$ , $B (2, - 7)$ , $D (0, - 3)$ . Find $C$ . $(3, - 5)$

Find sides, angles and diagonals of parallelograms
ABCD is a parallelogram. Find $m ∠ A B C$ . $114^{\circ}$
ABCD is a parallelogram. Find $A C$ . $6$
ABCD is a parallelogram. $A E = 5 x - 52$ and $A C = 3 x - 20$ . Find $A C$ . $16$

How to do these

In parallelogram $A B C D$ , $m ∠ A = {(3 x + 10)}^{\circ}$ and $m ∠ C = {(5 x - 20)}^{\circ}$ . Find $x$

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

The answer is $15$ .

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 $x$ . — a parallelogram with two consecutive angles marked → $8$
Sides: In parallelogram $A B C D$ , $A B = 3 x - 2$ and $C D = 5 x - 18$ . Find $x$ . → $8$
Diagonals: The diagonals of a parallelogram bisect: $A E = 3 x - 2$ and $E C = 5 x - 18$ . Find $x$ . → $8$
Rectangles, rhombuses and squares: The diagonals of rhombus $A B C D$ meet at $E$ , and $m ∠ A E B = {(5 x + 50)}^{\circ}$ . Find $x$ . → $8$
Find x and y: Find $x$ and $y$ so that $A B C D$ is a parallelogram: $A B = 2 x + 12$ , $C D = 3 x + 4$ , $A D = 4 y + 1$ , $B C = 2 y + 21$ . → $x = 8$ , $y = 10$
The missing vertex: Three vertices of parallelogram $A B C D$ are $A (- 1, 0)$ , $B (5, - 2)$ , $C (5, 3)$ . Find $D$ . → $(- 1, 5)$
Parallelograms: sides, angles and diagonals: ABCD is a parallelogram. Find $C D$ . — a quadrilateral abcd with its diagonals meeting at e, labeled A, B, C, D, 7, E → $7$

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 7: angles, sides, diagonals, rectangles, rhombuses and squares, find x and y, the missing vertex and parallelograms: sides, angles 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.

Properties of parallelograms worksheet

Find angles in a parallelogram

Use opposite sides of a parallelogram

Use the diagonals of a parallelogram

Find xxx and yyy in a parallelogram

Find the missing vertex of a parallelogram

Find sides, angles and diagonals of parallelograms

Find angles in a parallelogram

Use opposite sides of a parallelogram

Use the diagonals of a parallelogram

Find xxx and yyy in a parallelogram

Find the missing vertex of a parallelogram

Find sides, angles and diagonals of parallelograms

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these properties of parallelograms worksheets free?+

Do the properties of parallelograms worksheets come with an answer key?+

Are these properties of parallelograms worksheets printable?+

What grade are these properties of parallelograms worksheets for?+

Can I get a different version of the same properties of parallelograms worksheet?+

Is this a free alternative to Kuta Software for properties of parallelograms?+

Can I choose how hard the properties of parallelograms questions are?+

What kinds of question are on a properties of parallelograms worksheet?+

What do students get wrong with properties of parallelograms?+

Find $x$ and $y$ in a parallelogram

Find $x$ and $y$ in a parallelogram