Triangle congruence: ASA and AAS

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Two triangles, not to scale. Milo checks two tent flaps. △DFG ≅ △SUV by AAS, with m∠D = 48° and m∠F = 67°. In △SUV, m∠V = (3x + 5)°. What is x?

   20
2. 2.

   △CHQ with ∠C, ∠H and side HQ marked; △YWS with ∠S labeled (5x + 2)°. Noah checks two kite halves. △CHQ ≅ △YWS by AAS, with m∠C = 39° and m∠H = 84°. In △YWS, m∠S = (5x + 2)°. What is x?

   11
3. 3.

   Pia checks two boat sails. △GUW ≅ △FHD by AAS, with m∠G = 71° and m∠U = 45°. In △FHD, m∠D = (4x + 4)°. What is x?

   15
4. 4.

   “Two triangles, not to scale:” Ren checks two castle flags. △QVY ≅ △CGS by AAS, with m∠Q = 26° and m∠V = 92°. In △CGS, m∠S = (2x + 4)°. What is x?

   29
5. 5.

   Tala checks two bike-frame triangles. Only DF ∥ SU and DC = UC are marked. Is △DCF ≅ △UCS, and by which rule?

   • Yes, by ASA.
   • No: only one pair of sides is marked.
   • No: the triangles point in different directions.
   • No: equal angles alone prove only the same shape (AAA).
6. 6.

   Zee checks the two sides of a stepladder. Only DF ∥ SU and FC = SC are marked. Is △DCF ≅ △UCS, and by which rule?

   • No: only one pair of sides is marked.
   • Yes, by AAS.
   • No: the triangles point in different directions.
   • No: equal angles alone prove only the same shape (AAA).
7. 7.

   Bo checks two sandwich halves. Only ∠QHG = ∠QWG and ∠HQG = ∠WQG are marked. Is △HQG ≅ △WQG, and by which rule?

   • Yes, by AAS.
   • No: no pair of sides is marked.
   • Yes, by ASA.
   • No: the triangles point in different directions.
8. 8.

   Esme checks two window panes. The marks show which parts are equal. Which statement and rule are right?

   • △DFG ≅ △WCS by AAS
   • △DFG ≅ △CSW by ASA
   • △DFG ≅ △WCS by ASA
   • △DFG ≅ △WSC by ASA

9. Read this first

   Use this

   Two triangles, not to scale: triangle GQS on the left and triangle VUF on the right, turned. Marks: ∠Q and ∠U one arc; ∠S and ∠F two arcs; GQ and VU one tick. The matching table under them is blank.

10. 9.

    Kira checks two rug triangles. The marks show which parts are equal. Which statement and rule are right?

    • △GQS ≅ △VFU by AAS
    • △GQS ≅ △VUF by ASA
    • △GQS ≅ △VUF by AAS
    • △GQS ≅ △FUV by AAS

11. Use this

    Two triangles, not to scale: triangle HVY on the left and triangle QGD on the right, turned. Marks: ∠V and ∠G one arc; VY and GD one tick; ∠Y and ∠D two arcs. The matching table under them is blank.

12. 10.

    Luz checks two park shapes on a map. The marks show which parts are equal. Which statement and rule are right?

    • △HVY ≅ △QGD by ASA
    • △HVY ≅ △QDG by ASA
    • △HVY ≅ △DGQ by ASA
    • △HVY ≅ △QGD by AAS