Triangle congruence: SSS and SAS

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Kira checks two tent flaps. SAS needs the angle between two sides. Which angle of △CHQ is between sides CQ and HQ?

   • ∠C
   • ∠H
   • ∠Q
2. 2.

   Luz checks two kite halves. SAS needs the angle between two sides. Which angle of △SUW is between sides SU and SW?

   • ∠W
   • ∠U
   • ∠S
3. 3.

   Milo checks two boat sails. SAS needs the angle between two sides. Which angle of △GVY is between sides VY and GV?

   • ∠V
   • ∠Y
   • ∠G

4. Read this first

   Use this

   Two triangles, not to scale. △DFG: DF = 7 cm, FG = 10 cm, DG = 12 cm. △SUV: SV = 12 cm, SU = 7 cm, UV = 10 cm. The matching table under them lists the side rows of △DFG ≅ △SUV: DF ↔ SU, FG ↔ UV, DG ↔ SV.

5. 4.

   Noah checks two sandwich halves. The figure gives the sides of △DFG and △SUV. Is △DFG ≅ △SUV?

   • No: SSS also needs one pair of equal angles.
   • No: the sides are listed in a different order.
   • Yes, by SSS: all three pairs of sides are equal.

6. Use this

   Two triangles, not to scale. △GQU: GQ = 11 cm, QU = 6 cm, GU = 14 cm. △DCF: DF = 15 cm, DC = 11 cm, CF = 6 cm. The matching table under them lists the side rows of △GQU ≅ △DCF: GQ ↔ DC, QU ↔ CF, GU ↔ DF.

7. 5.

   Ren checks two paper triangles. The figure gives the sides of △GQU and △DCF. Is △GQU ≅ △DCF?

   • Yes, by SSS: GQ and QU match their partners.
   • No: SSS also needs one pair of equal angles.
   • No: GU = 14 cm but DF = 15 cm.
8. 6.

   Two triangles, not to scale. Tala checks two rug triangles. The figure gives the sides of △SVY and △HWG. Is △SVY ≅ △HWG?

   • Yes, by SSS: SV and SY match their partners.
   • No: VY = 12 cm but WG = 11 cm.
   • No: SSS also needs one pair of equal angles.
9. 7.

   Zee checks two kite halves, △DFG and △VSU. The matching table has ✓ on DF ↔ VS and FG ↔ SU. Which angle row needs a ✓ for SAS?

   • ∠F ↔ ∠U
   • ∠G ↔ ∠U
   • ∠D ↔ ∠V
   • ∠F ↔ ∠S
10. 8.

    Ari checks the two sides of a stepladder, △CHQ and △YWS. The matching table has ✓ on HQ ↔ WS and CQ ↔ YS. Which angle row needs a ✓ for SAS?

    • ∠H ↔ ∠W
    • ∠Q ↔ ∠S
    • ∠C ↔ ∠Y
    • ∠Q ↔ ∠Y
11. 9.

    Bo checks two boat sails, △GUW and △FDH. The matching table has ✓ on GU ↔ FD and GW ↔ FH. Which angle row needs a ✓ for SAS?

    • ∠G ↔ ∠D
    • ∠W ↔ ∠H
    • ∠G ↔ ∠F
    • ∠U ↔ ∠D
12. 10.

    Esme checks two bike-frame triangles, △QSY and △VCG. The matching table has ✓ on SY ↔ CG and QS ↔ VC. Which angle row needs a ✓ for SAS?

    • ∠Q ↔ ∠V
    • ∠S ↔ ∠G
    • ∠S ↔ ∠C
    • ∠Y ↔ ∠G