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10th grade Triangle congruence: ASA and AAS worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

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Triangle congruence: ASA and AAS

Grade 10 Math Worksheet - Challenge Me

NameDate

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

  1. Two triangles, not to scale. Milo checks two tent flaps. △DFG ≅ △SUV by AAS, with m∠D = 48° and m∠F = 67°. In △SUV, m∠V = (3x + 5)°. What is x?

  2. △CHQ with ∠C, ∠H and side HQ marked; △YWS with ∠S labeled (5x + 2)°. Noah checks two kite halves. △CHQ ≅ △YWS by AAS, with m∠C = 39° and m∠H = 84°. In △YWS, m∠S = (5x + 2)°. What is x?

  3. “Two triangles, not to scale:” Ren checks two castle flags. △QVY ≅ △CGS by AAS, with m∠Q = 26° and m∠V = 92°. In △CGS, m∠S = (2x + 4)°. What is x?

  4. Tala checks two bike-frame triangles. Only DF ∥ SU and DC = UC are marked. Is △DCF ≅ △UCS, and by which rule?

    • No: equal angles alone prove only the same shape (AAA).
    • Yes, by ASA.
    • No: the triangles point in different directions.
    • No: only one pair of sides is marked.

  5. Zee checks the two sides of a stepladder. Only DF ∥ SU and FC = SC are marked. Is △DCF ≅ △UCS, and by which rule?

    • No: only one pair of sides is marked.
    • No: equal angles alone prove only the same shape (AAA).
    • Yes, by AAS.
    • No: the triangles point in different directions.

  6. Ari checks two kite halves. Only ∠HQG = ∠WQG and ∠HGQ = ∠WGQ are marked. Is △HQG ≅ △WQG, and by which rule?

    • No: the triangles point in different directions.
    • Yes, by ASA.
    • Yes, by AAS.
    • No: no pair of sides is marked.

  7. Bo checks two sandwich halves. Only ∠QHG = ∠QWG and ∠HQG = ∠WQG are marked. Is △HQG ≅ △WQG, and by which rule?

    • No: no pair of sides is marked.
    • Yes, by AAS.
    • Yes, by ASA.
    • No: the triangles point in different directions.

  8. Esme checks two window panes. The marks show which parts are equal. Which statement and rule are right?

    • △DFG ≅ △WSC by ASA
    • △DFG ≅ △WCS by ASA
    • △DFG ≅ △WCS by AAS
    • △DFG ≅ △CSW by ASA

  9. “not to scale” Jun checks two quilt patches. The marks show which parts are equal. Which statement and rule are right?

    • △CHU ≅ △YSD by AAS
    • △CHU ≅ △YDS by ASA
    • △CHU ≅ △YDS by AAS
    • △CHU ≅ △DSY by AAS

  10. Read this first

    Use this

    Two triangles, not to scale: triangle HVY on the left and triangle QGD on the right, turned. Marks: ∠V and ∠G one arc; VY and GD one tick; ∠Y and ∠D two arcs. The matching table under them is blank.

  11. Luz checks two park shapes on a map. The marks show which parts are equal. Which statement and rule are right?

    • △HVY ≅ △QDG by ASA
    • △HVY ≅ △QGD by ASA
    • △HVY ≅ △QGD by AAS
    • △HVY ≅ △DGQ by ASA
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10th grade Triangle congruence: ASA and AAS worksheet – printable
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About this worksheet

Triangle congruence: ASA and AAS. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can say which side is between two angles, and tell ASA from AAS.
  • I can explain why two angles and any side are enough, but three angles are not.
  • I can use angles the figure gives (vertical, alternate interior, a shared side) to prove two triangles congruent.

Standard: G-CO.B.8

Words to know

ASA: Two angles and the side joining their corners prove congruence.

AAS: Two angles and a side not between them also prove it.

included side: The side whose two letters are the two angle corners.

AAA: Three equal angles: same shape, but maybe a different size. Not a rule.

alternate interior angles: Equal angles in a Z shape between parallel lines.

Common mistakes

Your child chose a side that touches only one of the two angles.

Your child added the two known angles and stopped.

Your child used 360° for the angles of a triangle.

What to say

Ask: which side joins the two corners?

Ask: what do the three angles of a triangle add to?

Ask: what do the angles of a triangle add to?

Questions parents ask

What is the most common mistake with triangle congruence: asa and aas?

Your child chose a side that touches only one of the two angles.

How can I help my child with triangle congruence: asa and aas?

Ask: which side joins the two corners?

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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