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.

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

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

   • Yes, by ASA.
   • Yes, by AAS.
   • No: the triangles point in different directions.
   • 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?

   • 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 ≅ △CSW by ASA
   • △DFG ≅ △WCS by ASA
   • △DFG ≅ △WCS by AAS
   • △DFG ≅ △WSC 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 ≅ △DSY by AAS
   • △CHU ≅ △YDS by AAS
   • △CHU ≅ △YDS by ASA
   • △CHU ≅ △YSD by AAS

10. 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.

11. 10.

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

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