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10th grade Triangle congruence: ASA and AAS worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Triangle congruence: ASA and AAS

Grade 10 Math Worksheet - Building Confidence

NameDate

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

  1. Pia checks two tent flaps. ASA needs the side between two angles. Which side of △SUW is between ∠S and ∠W?

    • SW
    • SU
    • UW

  2. Ren checks two quilt patches. ASA needs the side between two angles. Which side of △GVY is between ∠Y and ∠V?

    • GV
    • VY
    • GY

  3. “not to scale” Tala checks two castle flags, △DFG and △SUV. m∠D = m∠S = 52° and m∠F = m∠U = 71°. What is m∠V, in degrees?

  4. not to scale. Zee checks two sandwich halves, △CQW and △YHS. m∠C = m∠Y = 36° and m∠Q = m∠H = 97°. What is m∠S, in degrees?

  5. Ari checks two rug triangles, △GHU and △FDC. m∠G = m∠F = 64° and m∠H = m∠D = 61°. What is m∠C, in degrees?

  6. Bo checks two window panes, △SVY and △QGW. m∠S = m∠Q = 29° and m∠V = m∠G = 113°. What is m∠W, in degrees?

  8. Esme checks two paper triangles: ∠D = ∠U, DF = US, ∠F = ∠S. Do these facts prove △DFG ≅ △USV?

    • No: all three pairs of angles must be given.
    • No: all three pairs of sides must be given.
    • Yes, by AAS: the side is not between the angles.
    • Yes, by ASA: DF is between ∠D and ∠F.

  9. Jun checks two park shapes on a map: ∠H = ∠D, HW = DY, ∠W = ∠Y. Do these facts prove △CHW ≅ △QDY?

    Use the picture in question 7.

    • Yes, by ASA: HW is between ∠H and ∠W.
    • Yes, by AAS: the side is not between the angles.
    • No: all three pairs of sides must be given.
    • No: all three pairs of angles must be given.

  10. Kira checks the two sides of a stepladder: ∠G = ∠V, GS = VU, ∠S = ∠U. Do these facts prove △GQS ≅ △VFU?

    Use the picture in question 7.

    • Yes, by AAS: the side is not between the angles.
    • Yes, by ASA: GS is between ∠G and ∠S.
    • No: all three pairs of angles must be given.
    • No: all three pairs of sides must be given.

  11. Luz checks two bike-frame triangles: ∠V = ∠C, VY = CS, ∠Y = ∠S. Do these facts prove △UVY ≅ △HCS?

    Use the picture in question 7.

    • No: all three pairs of angles must be given.
    • Yes, by ASA: VY is between ∠V and ∠Y.
    • No: all three pairs of sides must be given.
    • Yes, by AAS: the side is not between the angles.
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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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