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Grade 10 · Math · Geometry

10th grade Triangle similarity: AA, SSS and SAS worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Triangle similarity: AA, SSS and SAS

Grade 10 Math Worksheet - Building Confidence

NameDate

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

  1. Jun compares two tent doors, △CDF and △QSU. Which rule proves △CDF ~ △QSU?

    • SSS~
    • SAS~
    • AA
    • Not enough to tell

  2. Kira compares two kite halves, △CDF and △QSU. Which rule proves △CDF ~ △QSU?

    • SSS~
    • AA
    • SAS~
    • Not enough to tell

  3. Luz compares two sails, △CDF and △QSU. Which rule proves △CDF ~ △QSU?

    • AA
    • SSS~
    • SAS~
    • Not enough to tell

  4. Milo compares two roof fronts, △CDF and △QSU. Which rule proves △CDF ~ △QSU?

    • Not enough to tell
    • AA
    • SSS~
    • SAS~

  5. Read this first

    Ratio table

    Columns small triangle | large triangle; rows shortest 4 | 8, middle 6 | 12, longest 7 | ?. Lengths in cm.

  6. Noah checks two triangle tiles and wants them similar by SSS~. The table pairs the sides by size. How long must the longest side of the large triangle be, in cm?

  7. Ratio table

    Columns small triangle | large triangle; rows shortest 6 | 10, middle 9 | 15, longest 10 | ?. Lengths in cm.

  8. Pia cuts two paper triangles for a mobile and wants them similar by SSS~. The table pairs the sides by size. How long must the longest side of the large triangle be, in cm?

  9. Ratio table

    Columns small triangle | large triangle; rows shortest 3 | 9, middle 5 | 15, longest 6 | ?. Lengths in cm.

  10. Ren plans a small and a big triangle kite and wants them similar by SSS~. The table pairs the sides by size. How long must the longest side of the large triangle be, in cm?

  11. Ratio table

    Columns small triangle | large triangle; rows shortest 8 | 10, middle 12 | 15, longest 14 | ?. Lengths in cm.

  12. Tala measures two triangle window panes and wants them similar by SSS~. The table pairs the sides by size. How long must the longest side of the large triangle be, in cm?

  13. Bo looks at a folding table from the side. CG and DF cross at Y, CD ∥ GF, and △YCD ~ △YGF by AA. How long is YG, in cm?

  14. Esme maps two parallel streets crossed by two roads. CG and DF cross at Y, CD ∥ GF, and △YCD ~ △YGF by AA. How long is YG, in cm?

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10th grade Triangle similarity: AA, SSS and SAS worksheet – printable
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About this worksheet

Similar triangles by AA, SSS and SAS. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can choose AA, SSS~ or SAS~, or say there is not enough to tell, from the marks on two triangles.
  • I can find the side that makes two triangles similar by SSS~ or SAS~, also when it is written with x.
  • I can find a missing side in a bowtie or a nested triangle, and describe the dilation and move that map one triangle onto the other.

Standard: G-SRT.A.3, G-SRT.B.5

Words to know

AA: Two pairs of equal angles: enough to make two triangles similar.

SSS~: All three pairs of sides share one scale factor.

SAS~: Two side ratios match, and the angle between those sides is equal.

included angle: The angle between two sides, at the corner where they meet.

bowtie: Two segments crossing at a point, with a parallel side at each end.

dilation: A move that makes a figure bigger or smaller by one scale factor.

Common mistakes

Your child called triangles similar by angle-angle with only one pair of equal angles.

Your child used SAS~ with an angle that is not between the two sides.

Your child thought more side lengths were needed when the facts given already prove similarity.

What to say

Ask: how many pairs of equal angles does AA need?

Ask: where must the equal angle sit for SAS~?

Ask: which rule, AA, SSS~ or SAS~, fits the facts you have?

Questions parents ask

What is the most common mistake with triangle similarity: aa, sss and sas?

Your child called triangles similar by angle-angle with only one pair of equal angles.

How can I help my child with triangle similarity: aa, sss and sas?

Ask: how many pairs of equal angles does AA need?

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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