Loading...
Use sequences of translations, rotations, reflections, and dilations to explain why figures are similar; apply angle-angle arguments; connect scale factor to side ratios; and verify similarity in maps, photos, and floor plans.
Aligned to 8.G.A.4, 8.G.A.5
Studying for a final? Geometry Final Exam Review or 8th Grade Math Final Exam Review
Share to Google Classroom (opens in a new tab)For parents & teachers
A research-backed week of short routines that help a student study less and remember more: spacing, self-quizzing, and a calmer week before tests.
Discover
Think about this
Why does doubling only the width of a photo break similarity with the original?
Equivalent ratios in similar shapes | 8th grade (TX) | Khan Academy (5:31)
Learn
Read each section like a formula card: why it matters, the steps, one worked example, then the check. Try the steps yourself before moving to Practice.
How to do it:
1. A dilation about a center multiplies every distance by
2. Corresponding angles stay equal; side lengths scale by
3. Map scale cm : km is a fixed factor relating drawing lengths to real lengths.
Worked example: A trail map uses cm for m. Map sides cm, cm, and cm become m, m, and m in the field. All three pairs share factor
Check: doubling only the width of a photo breaks similarity. Both dimensions need the same
How to do it:
1. Translate, rotate, or reflect to align corresponding parts.
2. If you can align the shape after scaling, the figures are similar.
3. Review Transformations & Similarity for coordinate rules.
Worked example: Reflect a floor-plan room, then dilate it to compare with a blueprint copy. The sequence (rigid plus dilation) is the similarity argument.
Check: rigid motions alone prove congruence, not similarity, unless
How to do it:
1. If two angles of one triangle match two angles of another, the triangles are similar (AA criterion).
2. Third angles must match because triangle angles sum to
3. Prefer AA when measuring every side would be messy.
Worked example: Triangles with angles -- in both figures are similar by AA. If one map angle is the field triangle shows the same angle at the matching corner.
Check: one pair of equal angles is not enough. You need two pairs (or one pair plus the consequence).
How to do it:
1. Matching sides sit opposite equal angles. Write ratios of corresponding sides equal to
2. Use the distance formula when coordinates are given.
3. A cropped photo blown up on a poster stays similar if width and height scale by the same factor.
Worked example: Small triangle sides match large sides so A photo cm by cm enlarged to cm wide must be cm tall.
Check: corresponding sides lie opposite equal angles; mixing the short of one triangle with the long of the other breaks the proportion. See Grade 7 Geometry for scale drawing foundations.
Practice
Apply what you read with the activities below. Use calculators and formula sheets as needed; scored quizzes are in Apply.
8 questions picked from what you need most
7 cards
1 matching · 1 fill-in
Your place saves as you go. Use Back to journey when you are ready to continue the path.
Apply
The best check is explaining Similarity Arguments with Transformations in your own words. The tutor listens like a curious friend and asks clarifying questions. No score, no grade.
Explain Similarity Arguments with Transformations as if to someone who has never heard of it. The tutor responds like a curious learner with clarifying questions, not a score.
Want a scored check? Open it here. The teach-back above does not require finishing it.
The scored check opens up once you have spent a little time in Learn and Practice. Recall sticks best after you have engaged with the material first.
