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

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

3. Read this first

   Use this

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

4. 3.

   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 ASA: two angles are enough.
   • Yes, by AAA: all three angles match.
   • No: AAA gives the same shape, not always the same size.
5. 4.

   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.
6. 5.

   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 AAA: all three angles match.
   • Yes, by ASA: two angles are enough.
   • No: AAA gives the same shape, not always the same size.
7. 6.

   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?

   • Yes, by AAA: the third angles match too.
   • No: the side is not between the two angles.
   • Yes, by AAS.
8. 7.

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

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

9. 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.

10. 8.

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

    • CQ = HY
    • ∠Q = ∠H
    • ∠C = ∠H
    • ∠Q = ∠Y
11. 9.

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

    • ∠H = ∠C
    • ∠S = ∠U
    • ∠S = ∠F
    • HS = CF
12. 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?

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