Triangle congruence: SSS and SAS

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Jun checks two kite halves. Only DF = DS (one tick) and FG = SG (two ticks) are marked. Is △DFG ≅ △DSG, and why?

   • Yes, by SSS: DG is a side of both triangles.
   • No: the two triangles face different ways.
   • No: only two pairs of parts are marked.
   • Yes, by SSA: two sides and an angle match.
2. 2.

   Kira checks two castle flags. Only QU = QW (one tick) and ∠UQC = ∠WQC (one arc) are marked. Is △QUC ≅ △QWC, and why?

   • No: the two triangles face different ways.
   • Yes, by SAS: QC is a side of both triangles.
   • No: only two pairs of parts are marked.
   • Yes, by SSA: two sides and an angle match.
3. 3.

   Luz checks two bike-frame triangles. Only GC = WC (one tick) and HC = YC (two ticks) are marked. Is △GCH ≅ △WCY, and why?

   • No: the two triangles face different ways.
   • Yes, by SAS: ∠GCH = ∠WCY, vertical angles.
   • No: no pair of angles is marked.
   • Yes, by SSA: two sides and an angle match.
4. 4.

   Milo checks the two sides of a stepladder. Only DV = QV (one tick) and SV = UV (two ticks) are marked. Is △DVS ≅ △QVU, and why?

   • No: the two triangles face different ways.
   • No: no pair of angles is marked.
   • Yes, by SAS: ∠DVS = ∠QVU, vertical angles.
   • Yes, by SSA: two sides and an angle match.
5. 5.

   Noah checks two tent flaps. DF = SU, FG = UV, m∠D = 46°, m∠G = 58° and m∠U = (2x + 6)°. What x gives △DFG ≅ △SUV by SAS?

   35
6. 6.

   Tala checks two quilt patches. QV = CS, VY = SG, m∠Q = 82°, m∠Y = 31° and m∠S = (5x + 2)°. What x gives △QVY ≅ △CSG by SAS?

   13
7. 7.

   not to scale. Zee checks two window panes. The marks show which parts are equal. Which statement and rule are right?

   • △DFG ≅ △WCS by SSS
   • △DFG ≅ △CSW by SSS
   • △DFG ≅ △WSC by SSS
   • △DFG ≅ △WCS by SAS
8. 8.

   “Two triangles, not to scale:” Ari checks two boat sails. The marks show which parts are equal. Which statement and rule are right?

   • △CHU ≅ △DSY by SAS
   • △CHU ≅ △YSD by SAS
   • △CHU ≅ △YDS by SSS
   • △CHU ≅ △YDS by SAS

9. Read this first

   Use this

   Two triangles, not to scale: triangle GQS on the left and triangle VUF on the right, turned. The matching table under them is blank.

10. 9.

    Bo checks two rug triangles. The marks show which parts are equal. Which statement and rule are right?

    • △GQS ≅ △VUF by SAS
    • △GQS ≅ △VUF by SSS
    • △GQS ≅ △VFU by SAS
    • △GQS ≅ △FUV by SAS
11. 10.

    not to scale; turned. Esme checks two castle flags. The marks show which parts are equal. Which statement and rule are right?

    • △HVY ≅ △QDG by SSS
    • △HVY ≅ △QGD by SSS
    • △HVY ≅ △QGD by SAS
    • △HVY ≅ △DGQ by SSS