Similarity and Dilations Worksheets, Grade 8 (8.G.A.4) – Free PDF + Answer Key

First page of the similarity and dilations practice worksheet

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Key idea

Similar = rigid motions and dilations. The test is equal ratios of corresponding sides. Differences do not test similarity: enlarging multiplies, so a long side gains more than a short one. Area scales by the square of the scale factor.

Sample problems

Write the definition of similar in terms of transformations.
Are 3, 4, 5 and 9, 12, 15 similar? Show the ratios.
Are 6, 8, 10 and 9, 12, 15 similar? Show the ratios.
Are 2, 3, 4 and 4, 5, 6 similar? Show the ratios and the differences.

Common mistakes to watch for

Checked only one pair. One matching ratio proves nothing — all of them have to agree.
Worked out only one of the two. Both are needed, because the whole point of item 3 is the contrast between them.
Said “you have to multiply, not add” without using the ratios. That is the right instinct and it is not yet the argument — the answer needs the three unequal ratios, and ideally the observation that a real enlargement's differences are unequal.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.