Which congruence rule applies? SSS, SAS, ASA, AAS, HL or not enough

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Tala checks two castle flags. Only CQ ⊥ HW and HQ = WQ are marked. Is △CQH ≅ △CQW, and by which rule?

   • No: only one pair of sides is marked.
   • Yes, by HL.
   • Yes, by SAS.
   • Not enough: no angle pair is marked.
2. 2.

   Zee checks two kite halves. Only ∠H = ∠W = 90° and QH = QW are marked. Is △QHC ≅ △QWC, and by which rule?

   • No: the kite has no marked angles.
   • No: SSA never proves congruence.
   • Yes, by HL.
   • Yes, by SAS.
3. 3.

   Ari checks two tower braces. Only GV ⊥ YU and VY = VU are marked. Is △GVY ≅ △GVU, and by which rule?

   • Yes, by SAS.
   • No: the right angle is marked only once.
   • No: SSA never proves congruence.
   • Yes, by HL.
4. 4.

   Bo checks two ramp sides. Right △DFG ≅ right △SUV by HL, right angle at F. DG = 41 cm, DF = 9 cm and UV = (4x + 12) cm. What is x?

   7
5. 5.

   Esme checks two tower braces. Right △CHW ≅ right △QYS by HL, right angle at W. CH = 61 cm, HW = 11 cm and QS = (5x + 15) cm. What is x?

   9
6. 6.

   Jun checks two ladder braces. Right △GQU ≅ right △DCF by HL, right angle at G. QU = 73 cm, GQ = 48 cm and DF = (3x + 4) cm. What is x?

   17
7. 7.

   Kira checks two tent flaps. Right △SVY ≅ right △HWC by HL, right angle at Y. SV = 85 cm, SY = 36 cm and WC = (4x + 5) cm. What is x?

   18
8. 8.

   Milo checks two quilt patches. In △CHQ, m∠C = 38°, m∠Q = 95°. In △WYS, m∠W = 38°, m∠Y = 47°. CQ = WS. Is △CHQ ≅ △WYS?

   • Not enough: only ∠C = ∠W is shown.
   • Yes, by AAA: the angles add to 180° in both.
   • Not enough: SSA.
   • Yes, by ASA: ∠C, CQ and ∠Q all match.
9. 9.

   Noah checks two window panes. In △GUW, m∠G = 64°, m∠U = 51°. In △DFH, m∠D = 64°, m∠H = 70°. GU = DF. Is △GUW ≅ △DFH?

   • Yes, by AAA: the angles add to 180° in both.
   • Yes, by ASA: ∠G, GU and ∠U match.
   • No: m∠U = 51° but m∠F = 46°.
   • Not enough: SSA.

10. Read this first

    Use this

    Two triangles, not to scale, with the given angles labeled and QS and CG one tick. The matching table under them is blank.

11. 10.

    Pia checks two rug triangles. In △QSY, m∠Q = 42°, m∠S = 77°. In △CGV, m∠C = 42°, m∠V = 66°. QS = CG. Is △QSY ≅ △CGV?

    • Not enough: SSA.
    • Yes, by ASA: ∠Q, QS and ∠S match.
    • Yes, by AAA: the angles add to 180° in both.
    • No: m∠S = 77° but m∠G = 72°.