Grade 10 · Math · Geometry

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 - Challenge Me

NameDate

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

1.
Ren checks two tent flaps. Only DG ⊥ FS and DF = DS are marked. Is △DGF ≅ △DGS, and by which rule?
- No: SSA never proves congruence.
- Yes, by SAS.
- Yes, by HL.
- No: only one pair of sides is marked.
2.
Tala checks two castle flags. Only CQ ⊥ HW and HQ = WQ are marked. Is △CQH ≅ △CQW, and by which rule?
- Yes, by HL.
- Not enough: no angle pair is marked.
- Yes, by SAS.
- No: only one pair of sides is marked.
3.
Zee checks two kite halves. Only ∠H = ∠W = 90° and QH = QW are marked. Is △QHC ≅ △QWC, and by which rule?
- Yes, by HL.
- Yes, by SAS.
- No: the kite has no marked angles.
- No: SSA never proves congruence.
4.
Ari checks two tower braces. Only GV ⊥ YU and VY = VU are marked. Is △GVY ≅ △GVU, and by which rule?
- Yes, by SAS.
- No: SSA never proves congruence.
- Yes, by HL.
- No: the right angle is marked only once.
Bo checks two ramp sides. Right △DFG ≅ right △SUV by HL, right angle at F. DG = 41 cm, DF = 9 cm and UV = (4x + 12) cm. What is x?
Esme checks two tower braces. Right △CHW ≅ right △QYS by HL, right angle at W. CH = 61 cm, HW = 11 cm and QS = (5x + 15) cm. What is x?
Jun checks two ladder braces. Right △GQU ≅ right △DCF by HL, right angle at G. QU = 73 cm, GQ = 48 cm and DF = (3x + 4) cm. What is x?
8.
Luz checks two park shapes on a map. In △DFG, m∠D = 50°, m∠F = 60°. In △SUV, m∠S = 50°, m∠V = 70°. DF = SU. Is △DFG ≅ △SUV?
- Yes, by AAA: the angles add to 180° in both.
- Yes, by ASA: ∠D, DF and ∠F all match.
- Not enough: SSA.
- Not enough: only ∠D = ∠S is shown.
9.
Milo checks two quilt patches. In △CHQ, m∠C = 38°, m∠Q = 95°. In △WYS, m∠W = 38°, m∠Y = 47°. CQ = WS. Is △CHQ ≅ △WYS?
- Yes, by AAA: the angles add to 180° in both.
- Yes, by ASA: ∠C, CQ and ∠Q all match.
- Not enough: SSA.
- Not enough: only ∠C = ∠W is shown.
10.
Noah checks two window panes. In △GUW, m∠G = 64°, m∠U = 51°. In △DFH, m∠D = 64°, m∠H = 70°. GU = DF. Is △GUW ≅ △DFH?
- Not enough: SSA.
- No: m∠U = 51° but m∠F = 46°.
- Yes, by ASA: ∠G, GU and ∠U match.
- Yes, by AAA: the angles add to 180° in both.

10th grade Which congruence rule applies? SSS, SAS, ASA, AAS, HL or not enough worksheet – printable — Print: 1 2 3 4 5 6

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.

More geometry

See all Geometry

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