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.

   “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
4. 4.

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

   • No: equal angles alone prove only the same shape (AAA).
   • Yes, by ASA.
   • No: the triangles point in different directions.
   • No: only one pair of sides is marked.
5. 5.

   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.
   • No: equal angles alone prove only the same shape (AAA).
   • Yes, by AAS.
   • No: the triangles point in different directions.
6. 6.

   Ari checks two kite halves. Only ∠HQG = ∠WQG and ∠HGQ = ∠WGQ are marked. Is △HQG ≅ △WQG, and by which rule?

   • No: the triangles point in different directions.
   • Yes, by ASA.
   • Yes, by AAS.
   • No: no pair of sides is marked.
7. 7.

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

   • No: no pair of sides is marked.
   • Yes, by AAS.
   • 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 ≅ △WSC by ASA
   • △DFG ≅ △WCS by ASA
   • △DFG ≅ △WCS by AAS
   • △DFG ≅ △CSW by ASA
9. 9.

   “not to scale” Jun checks two quilt patches. The marks show which parts are equal. Which statement and rule are right?

   • △CHU ≅ △YSD by AAS
   • △CHU ≅ △YDS by ASA
   • △CHU ≅ △YDS by AAS
   • △CHU ≅ △DSY by AAS

10. Read this first

    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.

11. 10.

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

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