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

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

   Two triangles, not to scale

   △GUW with UW and GW marked, ∠G and ∠U labeled; △DFH with FH and DH marked and ∠H labeled (4x + 5)°.

7. 6.

   Ren checks two park shapes on a map. UW = FH, GW = DH, m∠G = 37°, m∠U = 54° and m∠H = (4x + 5)°. What x gives △GUW ≅ △DFH by SAS?

   21
8. 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 SAS
   • △DFG ≅ △CSW by SSS
   • △DFG ≅ △WCS by SSS
   • △DFG ≅ △WSC by SSS
9. 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 ≅ △YDS by SAS
   • △CHU ≅ △YDS by SSS
   • △CHU ≅ △YSD by SAS

10. 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.

11. 9.

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

    • △GQS ≅ △FUV by SAS
    • △GQS ≅ △VFU by SAS
    • △GQS ≅ △VUF by SSS
    • △GQS ≅ △VUF by SAS
12. 10.

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

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