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?

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

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

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?

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

6. Use this

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

7. 5.

   Tala checks two castle flags: m∠D = m∠V = 50°, m∠F = m∠S = 60° and m∠G = m∠U = 70°. Do these facts prove △DFG ≅ △VSU?

   • Yes, by AAA: all three angles match.
   • Yes, by ASA: two angles are enough.
   • No: AAA gives the same shape, not always the same size.
8. 6.

   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 AAA: the third angles match too.
   • Yes, by AAS.
   • No: the side is not between the two angles.
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 AAA: the third angles match too.
   • Yes, by AAS.
10. 8.

    Esme checks the two sides of a stepladder. ∠D = ∠U and DF = US are marked. Which one more fact proves △DFG ≅ △USV by ASA?

    • ∠F = ∠U
    • ∠F = ∠S
    • FG = SV
    • ∠G = ∠V

11. 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.

12. 9.

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

    • ∠C = ∠H
    • ∠Q = ∠Y
    • ∠Q = ∠H
    • CQ = HY
13. 10.

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

    • HS = CF
    • ∠S = ∠U
    • ∠H = ∠C
    • ∠S = ∠F