Triangle congruence: ASA and AAS

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Milo checks two kite halves: m∠D = m∠S = 48°, DF = SU = 9 cm and m∠F = m∠U = 70°. Which is true about △DFG and △SUV?

   • Yes, by ASA.
   • No: all three pairs of sides must be given.
   • Yes, by AAS.
   • No: AAA is needed, so all three angles must be given.
2. 2.

   Noah checks two tent flaps: m∠C = m∠W = 41°, m∠H = m∠Y = 83° and HQ = YS = 12 cm. Which is true about △CHQ and △WYS?

   • No: the side is not between the two angles.
   • No: AAA is needed, so all three angles must be given.
   • Yes, by ASA.
   • Yes, by AAS.

3. Read this first

   Use this

   Two triangles, not to scale, with the given parts marked and labeled. The matching table for △GUW ≅ △DFH has ✓ on the three given rows.

4. 3.

   Pia checks two boat sails: m∠U = m∠F = 57°, m∠W = m∠H = 66° and GU = DF = 15 cm. Which is true about △GUW and △DFH?

   • Yes, by AAS.
   • Yes, by ASA.
   • No: the side is not between the two angles.
   • No: AAA is needed, so all three angles must be given.
5. 4.

   Ren checks two rug triangles: m∠S = m∠V = 38°, SY = VG = 11 cm and m∠Y = m∠G = 104°. Which is true about △QSY and △CVG?

   • Yes, by AAS.
   • No: all three pairs of sides must be given.
   • No: AAA is needed, so all three angles must be given.
   • Yes, by ASA.

6. Use this

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

7. 5.

   Zee checks two quilt patches: m∠C = m∠S = 44°, m∠H = m∠Y = 75° and CW = SQ = 10 cm. Do these facts prove △CHW ≅ △SYQ?

   • Yes, by AAS.
   • Yes, by AAA: the third angles match too.
   • No: the side is not between the two angles.
8. 6.

   Ari checks two window panes: m∠G = m∠H = 35°, m∠S = m∠Q = 65° and m∠U = m∠D = 80°. Do these facts prove △GSU ≅ △HQD?

   • Yes, by ASA: two angles are enough.
   • No: AAA gives the same shape, not always the same size.
   • Yes, by AAA: all three angles match.
9. 7.

   Bo checks two sandwich halves: m∠V = m∠W = 53°, m∠Y = m∠C = 68° and QV = FW = 14 cm. Do these facts prove △QVY ≅ △FWC?

   • No: the side is not between the two angles.
   • Yes, by AAS.
   • Yes, by AAA: the third angles match too.

10. Use this

    Two triangles, not to scale: triangle CQW and triangle HYD, with ∠W and ∠D one arc, QW and YD one tick. The matching table under them has (check) on those two rows.

11. 8.

    Jun checks two bike-frame triangles. ∠W = ∠D and QW = YD are marked. Which one more fact proves △CQW ≅ △HYD by ASA?

    • ∠Q = ∠H
    • ∠C = ∠H
    • CQ = HY
    • ∠Q = ∠Y
12. 9.

    Kira checks two paper triangles. ∠G = ∠U and GS = UF are marked. Which one more fact proves △GHS ≅ △UCF by ASA?

    • ∠S = ∠U
    • ∠H = ∠C
    • HS = CF
    • ∠S = ∠F
13. 10.

    “not to scale” Luz checks two park shapes on a map. ∠Y = ∠C and UY = QC are marked. Which one more fact proves △UVY ≅ △QSC by ASA?

    • ∠U = ∠Q
    • UV = QS
    • ∠U = ∠C
    • ∠V = ∠S