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?

   • No: only two pairs of parts are marked.
   • Yes, by SSS: DG is a side of both triangles.
   • No: the two triangles face different ways.
   • 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?

   • Yes, by SAS: QC 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.
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.
   • No: no pair of angles is marked.
   • Yes, by SSA: two sides and an angle match.
   • Yes, by SAS: ∠GCH = ∠WCY, vertical angles.

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

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