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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Read this first

    Use this

    Two triangles, not to scale, with the ticked parts marked. Under them, the matching table with one row per pair of parts and ✓ on the three rows named.

  2. Ren checks two quilt patches. The matching table for △DFG ≅ △SUV has ✓ on DF ↔ SU, ∠F ↔ ∠U and FG ↔ UV. Which rule do the ticked rows show?

    • SAS
    • Not enough
    • ASA
    • SSS

  3. Tala checks two tent flaps. The matching table for △CHQ ≅ △WYS has ✓ on ∠C ↔ ∠W, CH ↔ WY and ∠H ↔ ∠Y. Which rule do the ticked rows show?

    • AAS
    • Not enough
    • ASA
    • SSS

  4. Zee checks two bike-frame triangles. The matching table for △GUW ≅ △DFH has ✓ on UW ↔ FH, ∠W ↔ ∠H and GW ↔ DH. Which rule do the ticked rows show?

    • SSS
    • Not enough
    • SAS
    • ASA

  5. Bo checks two ramp sides. △DFG has a right angle at F. Which side of △DFG is the hypotenuse?

    • DG
    • DF
    • FG

  6. Esme checks two ladder braces. △CHW has a right angle at C. Which side of △CHW is the hypotenuse?

    • HW
    • CW
    • CH

  7. Jun checks two tower braces. △QSU has a right angle at U. Which side of △QSU is the hypotenuse?

    • QS
    • SU
    • QU

  8. Kira checks two kite halves. △GVY has a right angle at V. Which side of △GVY is the hypotenuse?

    • GY
    • GV
    • VY

  9. Luz checks two ramp sides. ∠F and ∠U are right angles, DG = SV and DF = SU. Do these facts prove △DFG ≅ △SUV?

    • Yes, by HL.
    • No: the third pair of sides must be given.
    • Yes, by SAS: the right angle is between the two sides.
    • No: this is SSA, and SSA never proves congruence.

  10. Milo checks two tower braces. ∠C and ∠Y are right angles, HQ = WS and CQ = YS. Do these facts prove △CHQ ≅ △YWS?

    • No: this is SSA, and SSA never proves congruence.
    • Yes, by HL.
    • No: the third pair of sides must be given.
    • Yes, by SAS: the right angle is between the two sides.

  11. Pia checks two sandwich halves. ∠Q and ∠C are right angles, VY = GS and QV = CG. Do these facts prove △QVY ≅ △CGS?

    • No: this is SSA, and SSA never proves congruence.
    • No: the third pair of sides must be given.
    • Yes, by HL.
    • Yes, by SAS: the right angle is between the two sides.
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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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