Triangle congruence: SSS and SAS

Answer Key - Grade 10 Math Worksheet

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

1. Read this first

   Use this

   Two triangles, not to scale, with the given parts marked and labeled. The matching table under them has ✓ on the three given rows.

2. 1.

   Jun checks two tent flaps: DF = SU = 9 cm, FG = UV = 12 cm and m∠F = m∠U = 40°. Do these facts prove △DFG ≅ △SUV?

   • No: the angle must be given before the sides.
   • Yes, by SAS: ∠F is between DF and FG.
   • No: SAS is not enough; all three sides must be given.
3. 2.

   Kira checks two quilt patches: CH = YQ = 14 cm, CW = YS = 10 cm and m∠C = m∠Y = 55°. Do these facts prove △CHW ≅ △YQS?

   • No: SAS is not enough; all three sides must be given.
   • No: the angle must be given before the sides.
   • Yes, by SAS: ∠C is between CH and CW.
4. 3.

   Luz checks two park shapes on a map: GQ = FD = 8 cm, QU = DH = 15 cm and m∠U = m∠H = 28°. Do these facts prove △GQU ≅ △FDH?

   • Yes, by SSA: two sides and an angle are equal.
   • No: ∠U is not between GQ and QU, so this is SSA.
   • Yes, by SAS: two sides and an angle are equal.
5. 4.

   Milo checks two castle flags: VY = GW = 11 cm, SY = CW = 13 cm and m∠S = m∠C = 48°. Do these facts prove △SVY ≅ △CGW?

   • Yes, by SSA: two sides and an angle are equal.
   • Yes, by SAS: two sides and an angle are equal.
   • No: ∠S is not between VY and SY, so this is SSA.
6. 5.

   Two triangles, not to scale. Ren checks two bike-frame triangles, △GUW and △DHF. The figure gives their sides, with DH = (4x + 4) cm. What x gives △GUW ≅ △DHF by SSS?

   6
7. 6.

   Two triangles, not to scale. The matching table under them is blank. Tala checks two boat sails, △QSV and △GYC. The figure gives their sides, with GC = (2x + 5) cm. What x gives △QSV ≅ △GYC by SSS?

   8

8. Use this

   Two triangles, not to scale:

9. 7.

   Zee checks two sandwich halves. DF = US and ∠F = ∠S are marked. Which one more fact proves △DFG ≅ △USV by SAS?

   • DG = UV
   • FG = SV
   • FG = UV
10. 8.

    Ari checks two window panes. QW = DY and ∠W = ∠Y are marked. Which one more fact proves △CQW ≅ △HDY by SAS?

    • CW = DY
    • CW = HY
    • CQ = HD
11. 9.

    Bo checks two rug triangles. GS = YU and ∠G = ∠Y are marked. Which one more fact proves △GHS ≅ △YFU by SAS?

    • GH = YF
    • GH = FU
    • HS = FU
12. 10.

    “not to scale” Esme checks two paper triangles. UY = SC and ∠U = ∠S are marked. Which one more fact proves △UVY ≅ △SQC by SAS?

    • VY = QC
    • UV = SQ
    • UV = QC