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.

   Ren checks two tent flaps. Only DG ⊥ FS and DF = DS are marked. Is △DGF ≅ △DGS, and by which rule?

   • No: SSA never proves congruence.
   • Yes, by SAS.
   • Yes, by HL.
   • No: only one pair of sides is marked.
2. 2.

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

   • Yes, by HL.
   • Not enough: no angle pair is marked.
   • Yes, by SAS.
   • No: only one pair of sides is marked.
3. 3.

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

   • Yes, by HL.
   • Yes, by SAS.
   • No: the kite has no marked angles.
   • No: SSA never proves congruence.
4. 4.

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

   • Yes, by SAS.
   • No: SSA never proves congruence.
   • Yes, by HL.
   • No: the right angle is marked only once.
5. 5.

   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
6. 6.

   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
7. 7.

   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
8. 8.

   Luz checks two park shapes on a map. In △DFG, m∠D = 50°, m∠F = 60°. In △SUV, m∠S = 50°, m∠V = 70°. DF = SU. Is △DFG ≅ △SUV?

   • Yes, by AAA: the angles add to 180° in both.
   • Yes, by ASA: ∠D, DF and ∠F all match.
   • Not enough: SSA.
   • Not enough: only ∠D = ∠S is shown.
9. 9.

   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?

   • Yes, by AAA: the angles add to 180° in both.
   • Yes, by ASA: ∠C, CQ and ∠Q all match.
   • Not enough: SSA.
   • Not enough: only ∠C = ∠W is shown.
10. 10.

    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?

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