Translations
Every vertex moves the same way. In Grade 4 with an arrow and in words, then with a column vector, and in Grade 9 finding the vector from a shape and its image.
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Teaching guide: transformations, similarity and Thales' theorem
Transformations (translations, reflections and rotations) move a shape without changing its shape or size; enlargements change its size but not its shape, which leads to similarity and Thales' theorem (the intercept theorem). This free generator builds A4 worksheets for Grades 4 to 9: shapes on a 4 mm grid to draw the image of, similar shapes and proportional segments drawn to scale, with an answer key that draws every image and writes out every calculation.
- For
- Elementary 4th, 5th, 6th · Middle & High 7th, 8th, 9th (ages 9-14)
- Subject
- Mathematics › Geometry & Measurement
- Includes
- Student sheet and answer key
- Format
- A4, to print or save as PDF; new exercises every time
- Price
- Free, no sign-up
- Available in
- Catalan, Spanish, English
Student worksheet 
Answer key Reflections
Each vertex and its image are the same distance from the mirror line. First vertical and horizontal lines, then shapes touching the line, and in Grade 9 diagonal lines.
Rotations
Half turns (180°) and quarter turns (90°) clockwise or anticlockwise, about a vertex or a point outside. The answer key joins the centre to a vertex and its image.
Combined transformations
Two transformations in a row. Two reflections in parallel lines make a translation; in perpendicular lines, a half turn about the point where they meet.
Enlargements
Draw the shape twice, three times or half as big, and from a centre of enlargement O with scale factor k, with the rays drawn in the answer key.
Similarity and Thales
The scale factor k, the missing sides, the perimeter times k and the area times k². Proportional segments between parallel lines and the shadow problem.
Frequently asked questions about transformations and similarity worksheets
Which grades are these worksheets for?
Grades 4 to 9 (Year 5 to Year 10). Translations with an arrow and reflections in vertical lines are for Grade 4; half turns for Grades 5 and 6; enlargements by 2 for Grade 6; column vectors, quarter turns and reductions for Grades 6 to 8; similar shapes and Thales' theorem for Grades 8 and 9; combined transformations, diagonal mirror lines and centres of enlargement for Grade 9.
What is in the answer key?
The image of every shape drawn in another colour on the same grid, with the vertices labelled A′, B′, C′; rotations join the centre to a vertex and its image, and enlargements from a centre show the rays. Similar shapes and Thales' theorem show every calculation: the scale factor, the proportion and the result.
Do the answers come out exactly?
Yes. Every vertex of an image lands on a grid point, and the sides and segments to find come out exactly, with at most one decimal place (two in the shadow problems). Every answer is worked out from the numbers printed on the sheet.
Are the similar shapes drawn to scale?
Yes. Both shapes are drawn at the same scale, so you can see how many times bigger one is, and the segments in the Thales drawings are in proportion too.
Where should pupils draw an enlargement with no centre?
Anywhere on the empty part of the grid: what matters is that every side is twice as long (or the scale factor given) and the shape stays the same. The answer key shows one possible position.
What other worksheets go well with these?
Symmetry on the grid for younger pupils, the coordinate plane for transformations with coordinates, map and plan scales, ratio and proportion, Pythagoras' theorem and trigonometry. Find every resource under maths worksheets.
How do I print only the answer key?
Click Print and choose "Answer key", or "Worksheet and answer key" for both. Your browser's print dialog can also save it as a PDF.
Is any pupil data sent anywhere?
No. Worksheets are generated in your browser and templates are saved in your browser's memory.
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