Similar polygons worksheet

Similar shapes have the same angles and sides in the same ratio. Find the scale factor from a pair you know, then apply it to the pair you do not.

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Sigma Prep · sigmaprep.io/worksheets Name Similar Polygons Date Period Find each missing side, or decide whether the polygons are similar. Find $x$ in similar figures The triangles are similar. Find $x$ . These triangles are similar. Solve for $x$ . The two triangles are similar. Find the length marked $x$ . The polygons are similar. Find $x$ . The polygons are similar. Find $x$ . These triangles are similar. Solve for $x$ . The two triangles are similar. Find the length marked $x$ . Test similarity and give the scale factor Is a triangle with sides 35, 30, 20 similar to a triangle with sides 8, 12, 14? If so, give the scale factor from the 8, 12, 14 triangle to the other. Rectangle A is 6 by 9. Rectangle B is 3 by 2. Are they similar? If so, give the scale factor from A to B. Is a 68 by 42 rectangle similar to an 11 by 7 rectangle? If so, give the scale factor from the 11 by 7 rectangle to the other. One triangle has sides 5, 5, 8 and another has sides 30, 30, 49. Are the triangles similar? If so, give the scale factor from the first to the second. A photo is 7 by 6, and a print made from it is 37 by 42. Is the print similar to the photo? If so, give the scale factor from the photo to the print. Triangle A has sides 5, 6, 8. Triangle B has sides 15, 18, 24. Are they similar? If so, give the scale factor from A to B. One rectangle measures 6 by 7 and another measures 14 by 12. Are the rectangles similar? If so, give the scale factor from the first to the second. Find $x$ in similar quadrilaterals The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ . The polygons are similar with scale factor $2 : 3$ (left to right). Find $x$ . The polygons are similar with scale factor $2 : 1$ (left to right). Find $x$ . The polygons are similar with scale factor $2 : 3$ (right to left). Find $x$ . The polygons are similar with scale factor $2 : 1$ (right to left). Find $x$ . The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Similar Polygons

Date Period

Find each missing side, or decide whether the polygons are similar.

Find $x$ in similar figures
The triangles are similar. Find $x$ .
These triangles are similar. Solve for $x$ .
The two triangles are similar. Find the length marked $x$ .
The polygons are similar. Find $x$ .
The polygons are similar. Find $x$ .
These triangles are similar. Solve for $x$ .
The two triangles are similar. Find the length marked $x$ .

Test similarity and give the scale factor
Is a triangle with sides 35, 30, 20 similar to a triangle with sides 8, 12, 14? If so, give the scale factor from the 8, 12, 14 triangle to the other.
Rectangle A is 6 by 9. Rectangle B is 3 by 2. Are they similar? If so, give the scale factor from A to B.
Is a 68 by 42 rectangle similar to an 11 by 7 rectangle? If so, give the scale factor from the 11 by 7 rectangle to the other.
One triangle has sides 5, 5, 8 and another has sides 30, 30, 49. Are the triangles similar? If so, give the scale factor from the first to the second.
A photo is 7 by 6, and a print made from it is 37 by 42. Is the print similar to the photo? If so, give the scale factor from the photo to the print.
Triangle A has sides 5, 6, 8. Triangle B has sides 15, 18, 24. Are they similar? If so, give the scale factor from A to B.
One rectangle measures 6 by 7 and another measures 14 by 12. Are the rectangles similar? If so, give the scale factor from the first to the second.

Find $x$ in similar quadrilaterals
The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ .
The polygons are similar with scale factor $2 : 3$ (left to right). Find $x$ .
The polygons are similar with scale factor $2 : 1$ (left to right). Find $x$ .
The polygons are similar with scale factor $2 : 3$ (right to left). Find $x$ .
The polygons are similar with scale factor $2 : 1$ (right to left). Find $x$ .
The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ .



Sigma Prep · sigmaprep.io/worksheets Name Similar PolygonsAnswer keyVersion 1 Date Period Find each missing side, or decide whether the polygons are similar. Find $x$ in similar figures The triangles are similar. Find $x$ . $2$ These triangles are similar. Solve for $x$ . $8$ The two triangles are similar. Find the length marked $x$ . $6$ The polygons are similar. Find $x$ . $14$ The polygons are similar. Find $x$ . $10$ These triangles are similar. Solve for $x$ . $9$ The two triangles are similar. Find the length marked $x$ . $5$ Test similarity and give the scale factor Is a triangle with sides 35, 30, 20 similar to a triangle with sides 8, 12, 14? If so, give the scale factor from the 8, 12, 14 triangle to the other.Yes, scale factor $\frac{5}{2}$ Rectangle A is 6 by 9. Rectangle B is 3 by 2. Are they similar? If so, give the scale factor from A to B.Yes, scale factor $\frac{1}{3}$ Is a 68 by 42 rectangle similar to an 11 by 7 rectangle? If so, give the scale factor from the 11 by 7 rectangle to the other.No; $6 \neq \frac{68}{11}$ One triangle has sides 5, 5, 8 and another has sides 30, 30, 49. Are the triangles similar? If so, give the scale factor from the first to the second.No; $6 \neq \frac{49}{8}$ A photo is 7 by 6, and a print made from it is 37 by 42. Is the print similar to the photo? If so, give the scale factor from the photo to the print.No; $\frac{37}{6} \neq 6$ Triangle A has sides 5, 6, 8. Triangle B has sides 15, 18, 24. Are they similar? If so, give the scale factor from A to B.Yes, scale factor $3$ One rectangle measures 6 by 7 and another measures 14 by 12. Are the rectangles similar? If so, give the scale factor from the first to the second.Yes, scale factor $2$ Find $x$ in similar quadrilaterals The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ . $12$ The polygons are similar with scale factor $2 : 3$ (left to right). Find $x$ . $24$ The polygons are similar with scale factor $2 : 1$ (left to right). Find $x$ . $3$ The polygons are similar with scale factor $2 : 3$ (right to left). Find $x$ . $18$ The polygons are similar with scale factor $2 : 1$ (right to left). Find $x$ . $4$ The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ . $16$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Similar PolygonsAnswer keyVersion 1

Date Period

Find each missing side, or decide whether the polygons are similar.

Find $x$ in similar figures
The triangles are similar. Find $x$ . $2$
These triangles are similar. Solve for $x$ . $8$
The two triangles are similar. Find the length marked $x$ . $6$
The polygons are similar. Find $x$ . $14$
The polygons are similar. Find $x$ . $10$
These triangles are similar. Solve for $x$ . $9$
The two triangles are similar. Find the length marked $x$ . $5$

Test similarity and give the scale factor
Is a triangle with sides 35, 30, 20 similar to a triangle with sides 8, 12, 14? If so, give the scale factor from the 8, 12, 14 triangle to the other.Yes, scale factor $\frac{5}{2}$
Rectangle A is 6 by 9. Rectangle B is 3 by 2. Are they similar? If so, give the scale factor from A to B.Yes, scale factor $\frac{1}{3}$
Is a 68 by 42 rectangle similar to an 11 by 7 rectangle? If so, give the scale factor from the 11 by 7 rectangle to the other.No; $6 \neq \frac{68}{11}$
One triangle has sides 5, 5, 8 and another has sides 30, 30, 49. Are the triangles similar? If so, give the scale factor from the first to the second.No; $6 \neq \frac{49}{8}$
A photo is 7 by 6, and a print made from it is 37 by 42. Is the print similar to the photo? If so, give the scale factor from the photo to the print.No; $\frac{37}{6} \neq 6$
Triangle A has sides 5, 6, 8. Triangle B has sides 15, 18, 24. Are they similar? If so, give the scale factor from A to B.Yes, scale factor $3$
One rectangle measures 6 by 7 and another measures 14 by 12. Are the rectangles similar? If so, give the scale factor from the first to the second.Yes, scale factor $2$

Find $x$ in similar quadrilaterals
The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ . $12$
The polygons are similar with scale factor $2 : 3$ (left to right). Find $x$ . $24$
The polygons are similar with scale factor $2 : 1$ (left to right). Find $x$ . $3$
The polygons are similar with scale factor $2 : 3$ (right to left). Find $x$ . $18$
The polygons are similar with scale factor $2 : 1$ (right to left). Find $x$ . $4$
The polygons are similar with scale factor $1 : 2$ (right to left). Find $x$ . $16$

How to do these

Sides $6$ and $9$ match. Another side is $8$

The scale factor is 9 over 6.
That is one and a half.
Eight times that is 12.

The answer is $12$ .

Where students go wrong

Pairing sides by where they sit on the page rather than by the angles they are between. Similar shapes get drawn turned round, and the matching has to follow the letters, not the picture.

Also called corresponding sides.

What you can put on this worksheet

Matching sides, from the diagram: These triangles are similar. Solve for $x$ . — two similar triangles, labeled x, 5, 8, 10 → $4$
Are they similar? The scale factor: A photo is 2 by 5, and a print made from it is 20 by 8. Is the print similar to the photo? If so, give the scale factor from the photo to the print. → Yes, scale factor $4$
Similar quadrilaterals: The polygons are similar. Find $x$ . — two quadrilaterals, labeled 14, 10, x, 20 → $28$
Sides in proportion, but do the angles match?: Parallelogram 1: sides 12 and 9, one angle $52^{\circ}$ . Parallelogram 2: sides 16 and 12, one angle $52^{\circ}$ . Are they similar? If so, give the ratio of their sides, small : large. → Similar, $3 : 4$
The scale factor when one figure is turned or flipped: The figures are similar. What scale factor takes the larger one to the smaller one? — two quadrilaterals, labeled 12, 9, 16 → $\frac{3}{4}$
One figure turned or flipped: find x: $W X Y Z$ is a scaled copy of $A B C D$ , turned or flipped. What is $x$ ? — two quadrilaterals → $20$

Questions about these worksheets

Yes. Every similar polygons 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 similar polygons 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 6: matching sides, from the diagram, are they similar? the scale factor, similar quadrilaterals, sides in proportion, but do the angles match?, the scale factor when one figure is turned or flipped and one figure turned or flipped: find x. Tick as many as you want and set how many of each, or let it spread them evenly.

Pairing sides by where they sit on the page rather than by the angles they are between. Similar shapes get drawn turned round, and the matching has to follow the letters, not the picture.

Similar polygons worksheet

Find xxx in similar figures

Test similarity and give the scale factor

Find xxx in similar quadrilaterals

Find xxx in similar figures

Test similarity and give the scale factor

Find xxx in similar quadrilaterals

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these similar polygons worksheets free?+

Do the similar polygons worksheets come with an answer key?+

Are these similar polygons worksheets printable?+

What grade are these similar polygons worksheets for?+

Can I get a different version of the same similar polygons worksheet?+

Is this a free alternative to Kuta Software for similar polygons?+

Can I choose how hard the similar polygons questions are?+

What kinds of question are on a similar polygons worksheet?+

What do students get wrong with similar polygons?+

Find $x$ in similar figures

Find $x$ in similar quadrilaterals

Find $x$ in similar figures

Find $x$ in similar quadrilaterals