PencilGo

Grade 10 · Math · Geometry

10th grade Triangle congruence: SSS and SAS worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version
Print

Triangle congruence: SSS and SAS

Grade 10 Math Worksheet - Challenge Me

NameDate

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

  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. 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. 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. 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. 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?

  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. 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?

  8. 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. “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. 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. 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
PencilGopencilgo.com

10th grade Triangle congruence: SSS and SAS worksheet – printable
Print: 123456

About this worksheet

Triangle congruence: SSS and SAS. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can say which angle is between two sides, and tell SAS from SSA.
  • I can decide whether the facts given prove two triangles congruent by SSS or SAS.
  • I can find the missing fact or the value of x that makes SSS or SAS work, including a side two triangles share.

Standard: G-CO.B.8

Words to know

SSS: Three pairs of equal sides prove two triangles congruent.

SAS: Two pairs of sides and the angle between them prove it.

included angle: The angle where two sides meet; its letter is in both side names.

SSA: Two sides and an angle not between them: not a rule, proves nothing.

shared side: One segment that belongs to both triangles; it matches itself.

vertical angles: Angles across from each other where two lines cross; always equal.

Common mistakes

Your child used an angle that is not between the two sides.

Your child thought three pairs of equal sides were not enough. Build two triangles from the same three straws and see they always match.

Your child checked two pairs of sides and stopped.

What to say

Ask: at which corner do the two sides meet?

Ask: does SSS need two pairs or three?

Questions parents ask

What is the most common mistake with triangle congruence: sss and sas?

Your child used an angle that is not between the two sides.

How can I help my child with triangle congruence: sss and sas?

Ask: at which corner do the two sides meet?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records

Ready for easier practice?

Print a sheet, scan it when it’s done, and PencilGo picks the next one.

Create a free account