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

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Two triangles, not to scale, with the ticked parts marked. Under them, the matching table with one row per pair of parts and ✓ on the three rows named.

2. 1.

   Ren checks two quilt patches. The matching table for △DFG ≅ △SUV has ✓ on DF ↔ SU, ∠F ↔ ∠U and FG ↔ UV. Which rule do the ticked rows show?

   • SSS
   • ASA
   • SAS
   • Not enough
3. 2.

   Zee checks two bike-frame triangles. The matching table for △GUW ≅ △DFH has ✓ on UW ↔ FH, ∠W ↔ ∠H and GW ↔ DH. Which rule do the ticked rows show?

   • Not enough
   • SAS
   • ASA
   • SSS
4. 3.

   Ari checks two castle flags. The matching table for △QSY ≅ △CVG has ✓ on ∠Q ↔ ∠C, ∠S ↔ ∠V and SY ↔ VG. Which rule do the ticked rows show?

   • SSS
   • Not enough
   • ASA
   • AAS
5. 4.

   Bo checks two ramp sides. △DFG has a right angle at F. Which side of △DFG is the hypotenuse?

   • DG
   • FG
   • DF
6. 5.

   Esme checks two ladder braces. △CHW has a right angle at C. Which side of △CHW is the hypotenuse?

   • HW
   • CW
   • CH
7. 6.

   Kira checks two kite halves. △GVY has a right angle at V. Which side of △GVY is the hypotenuse?

   • VY
   • GY
   • GV
8. 7.

   Luz checks two ramp sides. ∠F and ∠U are right angles, DG = SV and DF = SU. Do these facts prove △DFG ≅ △SUV?

   • No: the third pair of sides must be given.
   • Yes, by SAS: the right angle is between the two sides.
   • Yes, by HL.
   • No: this is SSA, and SSA never proves congruence.
9. 8.

   Milo checks two tower braces. ∠C and ∠Y are right angles, HQ = WS and CQ = YS. Do these facts prove △CHQ ≅ △YWS?

   • No: this is SSA, and SSA never proves congruence.
   • No: the third pair of sides must be given.
   • Yes, by HL.
   • Yes, by SAS: the right angle is between the two sides.
10. 9.

    Noah checks two ladder braces. ∠W and ∠F are right angles, GU = HD and GW = HF. Do these facts prove △GUW ≅ △HDF?

    • Yes, by SAS: the right angle is between the two sides.
    • No: the third pair of sides must be given.
    • Yes, by HL.
    • No: this is SSA, and SSA never proves congruence.
11. 10.

    Pia checks two sandwich halves. ∠Q and ∠C are right angles, VY = GS and QV = CG. Do these facts prove △QVY ≅ △CGS?

    • Yes, by SAS: the right angle is between the two sides.
    • No: this is SSA, and SSA never proves congruence.
    • Yes, by HL.
    • No: the third pair of sides must be given.