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10th grade Similar figures: corresponding sides, scale factor, and all circles are similar worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Similar figures: corresponding sides, scale factor, and all circles are similar

Grade 10 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

  1. Ari checks pairs of shapes by their side lengths, all in cm. Which pair is similar?

    • Triangles with sides 6, 8, 10 and 9, 12, 15
    • Triangles with sides 4, 6, 8 and 6, 9, 11
    • Triangles with sides 3, 4, 5 and 6, 7, 8
    • Right triangles with sides 3, 4, 5 and 5, 12, 13

  2. Bo checks pairs of shapes by their side lengths, all in cm. Which pair is similar?

    • Rectangles 4 by 6 and 10 by 15
    • Rectangles 3 by 5 and 6 by 8, with 90° angles
    • Rectangles 5 by 7 and 8 by 10
    • Rectangles 2 by 3 and 4 by 7

  3. Jun checks pairs of shapes by their side lengths, all in cm. Which pair is similar?

    • A 5 by 5 square and a 5 by 10 rectangle
    • Rectangles 8 by 10 and 12 by 16
    • Rectangles 9 by 12 and 6 by 8
    • Rectangles 6 by 9 and 9 by 12

  4. Kira scales a boat drawing. △CDF ~ △UQS, with CD = 6, DF = 8, CF = 10 (cm). QS = 20 cm. What is the scale factor from △CDF to △UQS?

  5. Luz scales a ramp drawing. △CDF ~ △SUQ, with CD = 4, DF = 6, CF = 8 (cm). SQ = 14 cm. What is the scale factor from △CDF to △SUQ?

  6. Milo scales a star drawing. △UQS ~ △CDF, with UQ = 15, QS = 20, US = 25 (cm). DF = 8 cm. What is the scale factor from △UQS to △CDF?

  7. Noah scales a park drawing. △CDF ~ △QSU, with CD = 9, DF = 12, CF = 15 (cm). SU = 20 cm. What is the scale factor from △CDF to △QSU?

  8. Pia scales a house plan. △CDF ~ △UQS, with CD = 6 and DF = 10 in the first triangle. UQ = 15. How long is QS?

  9. Ren scales a cheese plan. △CDF ~ △UQS, with CD = 4 and DF = 6 in the first triangle. UQ = 12. How long is QS?

  10. Tala scales a pizza plan. △CDF ~ △UQS, with CD = 8 and DF = 12 in the first triangle. UQ = 6. How long is QS?

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10th grade Similar figures: corresponding sides, scale factor, and all circles are similar worksheet – printable
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About this worksheet

Similar figures and the scale factor. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can decide whether two figures are similar by AA, SAS~ or SSS~, and say what is missing when the facts are not enough.
  • I can use the triangle proportionality theorem and its converse, and set up similar triangles for a height or a distance I cannot measure.
  • I can say which dilation and rigid motions carry one figure onto a similar one, and why lengths grow by k, areas by k × k and volumes by k × k × k.

Standard: G-SRT.A.2, G-C.A.1

Words to know

similar (~): Same shape, maybe a different size: angles match and sides grow by one number.

similarity statement: △CDF ~ △UQS: letters in the same place go together (C with U, D with Q).

scale factor: The number every length is multiplied by, from the first figure to the second.

congruent: Same shape and same size: similar with scale factor 1.

circumference: The distance around a circle.

perimeter: The distance around a triangle: all three sides added.

dilation: A move that multiplies every distance from a center by the scale factor.

Common mistakes

Your child saw every side grow by the same amount and called the shapes similar. Similar sides grow by the same ratio, not the same amount.

Your child checked some pairs of sides and stopped.

Your child decided from the angles alone. Rectangles all have 90° angles, so the sides must also be in one ratio.

What to say

Ask: do all the pairs make the same ratio?

Questions parents ask

What is the most common mistake with similar figures: corresponding sides, scale factor, and all circles are similar?

Your child saw every side grow by the same amount and called the shapes similar. Similar sides grow by the same ratio, not the same amount.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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