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

   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?

   • Yes, by SSA: two sides and an angle match.
   • No: no pair of angles is marked.
   • No: the two triangles face different ways.
   • Yes, by SAS: ∠DVS = ∠QVU, vertical angles.
3. 3.

   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

4. Read this first

   Use this

   Two triangles, not to scale: triangle CHQ with CH and CQ marked, ∠H and ∠Q labeled; triangle WYS with WY and WS marked and ∠W labeled.

5. 4.

   Pia checks two sandwich halves. CH = WY, CQ = WS, m∠H = 35°, m∠Q = 95° and m∠W = (3x + 8)°. What x gives △CHQ ≅ △WYS by SAS?

   14

6. 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. 5.

   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. 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
9. 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 ≅ △WSC by SSS
   • △DFG ≅ △WCS by SAS
   • △DFG ≅ △CSW by SSS
10. 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 ≅ △YDS by SAS
    • △CHU ≅ △YDS by SSS
    • △CHU ≅ △YSD by SAS
    • △CHU ≅ △DSY by SAS

11. 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.

12. 9.

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

    • △GQS ≅ △VFU by SAS
    • △GQS ≅ △FUV by SAS
    • △GQS ≅ △VUF by SAS
    • △GQS ≅ △VUF by SSS
13. 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 ≅ △QDG by SSS
    • △HVY ≅ △QGD by SSS
    • △HVY ≅ △QGD by SAS