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10th grade Which congruence rule applies? SSS, SAS, ASA, AAS, HL or not enough worksheet

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Which congruence rule applies? SSS, SAS, ASA, AAS, HL or not enough

Grade 10 Math Worksheet

NameDate

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

  1. Read this first

    Use this

    Two triangles, not to scale, with the given parts marked and labeled.

  2. Ren checks two rug triangles: DF = SU = 10 cm, FG = UV = 14 cm and m∠G = m∠V = 36°. Which rule proves them congruent, if any?

    • Yes, by SAS.
    • Yes, by HL.
    • Yes, by SSA.
    • Not enough: this is SSA.

  3. Tala checks two paper triangles: CH = QY = 13 cm, CW = QS = 8 cm and m∠H = m∠Y = 34°. Which rule proves them congruent, if any?

    • Yes, by SAS.
    • Yes, by SSA.
    • Not enough: this is SSA.
    • Yes, by HL.

  4. Use this

    Two triangles, not to scale, with the given angles marked and labeled.

  5. Zee checks two window panes: m∠G = m∠F = 45°, m∠Q = m∠D = 55° and m∠U = m∠C = 80°. Which rule proves △GQU ≅ △FDC, if any?

    • Yes, by AAA.
    • Not enough: AAA fixes the shape, not the size.
    • Yes, by ASA.

  6. Ari checks two boat sails: m∠S = m∠H = 30°, m∠V = m∠W = 64° and m∠Y = m∠G = 86°. Which rule proves △SVY ≅ △HWG, if any?

    • Not enough: AAA fixes the shape, not the size.
    • Yes, by ASA.
    • Yes, by AAA.

  7. Esme checks two tower braces. Right △CHQ ≅ right △SWY by HL, with the right angle at H. CQ = 37 cm and HQ = 12 cm. How long is SW, in cm?

  8. Jun checks two ladder braces. Right △GUW ≅ right △FHD by HL, with the right angle at G. UW = 53 cm and GU = 28 cm. How long is FD, in cm?

  9. Kira checks two kite halves. Right △QSV ≅ right △YCG by HL, with the right angle at S. QV = 65 cm and SV = 33 cm. How long is YC, in cm?

  10. Luz checks two tower braces. ∠F and ∠V are right angles, and DF = SV. Which one more fact proves △DFG ≅ △SVU by HL?

    • DG = SU
    • ∠G = ∠U
    • DG = SV
    • FG = VU

  11. Noah checks two tent flaps. ∠S and ∠F are right angles, and GS = UF. Which one more fact proves △GHS ≅ △UCF by HL?

    • HS = CF
    • ∠H = ∠C
    • GH = UC
    • GH = CF

  12. Pia checks two ladder braces. ∠V and ∠Q are right angles, and UV = DQ. Which one more fact proves △UVY ≅ △DQC by HL?

    • UY = DC
    • ∠Y = ∠C
    • UY = QC
    • VY = QC
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10th grade Which congruence rule applies? SSS, SAS, ASA, AAS, HL or not enough worksheet – printable
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About this worksheet

Choosing a congruence rule, and HL. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can name the rule a set of facts shows, or say "not enough" for SSA and AAA.
  • I can find the hypotenuse and use HL for right triangles.
  • I can use HL and the Pythagorean theorem to find a side, and find missing angles before I choose a rule.

Standard: G-CO.B.8, G-SRT.B.5

Words to know

hypotenuse: The side across from the right angle; the longest side.

leg: One of the two sides that make the right angle.

HL: Hypotenuse and one leg equal in two right triangles prove congruence.

not enough: The facts fit two different triangles, so no rule applies.

SSA, AAA: Patterns that are not rules (SSA works only as HL).

Common mistakes

Your child named a rule with the sides and angles swapped (ASA for SAS).

Your child mixed up ASA (the side is between the two angles) and AAS (it is not).

Your child thought only three equal sides can prove triangles congruent.

What to say

Ask: how many of the ticked parts are sides?

Ask: does the side join the two angle corners?

Ask: which other rules do you know?

Questions parents ask

What is the most common mistake with which congruence rule applies? sss, sas, asa, aas, hl or not enough?

Your child named a rule with the sides and angles swapped (ASA for SAS).

How can I help my child with which congruence rule applies? sss, sas, asa, aas, hl or not enough?

Ask: how many of the ticked parts are sides?

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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