Triangle congruence: ASA and AAS

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   Milo checks two kite halves. ASA needs the side between two angles. Which side of △DFG is between ∠D and ∠F?

   • DG
   • FG
   • DF
2. 2.

   Noah checks two boat sails. ASA needs the side between two angles. Which side of △CHQ is between ∠Q and ∠H?

   • CQ
   • CH
   • HQ
3. 3.

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

   • SU
   • SW
   • UW
4. 4.

   “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?

   57
5. 5.

   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?

   47
6. 6.

   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?

   55
8. 7.

   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.
   • Yes, by ASA: DF is between ∠D and ∠F.
   • No: all three pairs of sides must be given.
   • Yes, by AAS: the side is not between the angles.
9. 8.

   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.

   • No: all three pairs of angles must be given.
   • 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.
10. 9.

    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.

    • No: all three pairs of angles must be given.
    • Yes, by ASA: GS is between ∠G and ∠S.
    • Yes, by AAS: the side is not between the angles.
    • No: all three pairs of sides must be given.
11. 10.

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

    Use the picture in question 7.

    • 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.
    • Yes, by ASA: VY is between ∠V and ∠Y.