Triangle congruence criteria · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Proving triangles congruent

Mathematics · Geometry · ages 12-14
Name ______________________   Date ____________

  1. Triangle ABC is congruent to triangle DEF. Which side matches side BC?

    • DE
    • EF
    • FD

  2. In triangle ABC, which side sits opposite angle C?

    • Side a
    • Side c
    • Side b

  3. Triangle ABC is congruent to triangle DEF. Side AB is 9 cm long. How long is side DE?

    Answer: ______________

  4. Two triangles have all three pairs of sides equal in length. Which congruence criterion applies?

    • SSS
    • ASA
    • RHS

  5. Two right triangles have matching hypotenuses of 10 cm and one matching side of 6 cm. Which criterion proves them congruent?

    • SAS
    • ASA
    • RHS

  6. For SAS, how many sides need to match exactly (not counting the angle)?

    • 1
    • 2
    • 3

  7. Triangle ABC is congruent to triangle DEF. Angle B in triangle ABC measures 60 degrees. What does angle E measure in triangle DEF?

    Answer: ______________

  8. Triangle PQR has angle P = 40 degrees, angle Q = 70 degrees, and side PQ = 6 cm. Triangle XYZ has angle X = 40 degrees, angle Y = 70 degrees, and side XY = 6 cm. Which criterion proves they are congruent?

    • ASA
    • SAS
    • SSS

  9. A triangle has sides 6 cm and 8 cm, and a 40 degree angle opposite the 6 cm side. Does this fix exactly one possible triangle?

    • Yes, exactly one triangle always fits
    • No, no triangle can be made
    • No, more than one triangle can fit these measurements

  10. A triangle has sides 5 cm and 7 cm. The third side must be shorter than the other two added together. What is the longest whole number of centimetres the third side can be?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Proving triangles congruent W1-mt_167X6Ax8P7-s1

  1. EF · B matches E and C matches F, so side BC matches side EF.
  2. Side c · Each side's lowercase letter matches the vertex it sits across from. Side c shares its letter with vertex C, so side c is opposite angle C.
  3. 9 · A matches D and B matches E, so side AB matches side DE. Congruent triangles have equal corresponding sides, so DE is 9 cm.
  4. SSS · When every side matches, that is SSS: side-side-side.
  5. RHS · Both triangles have a right angle, the hypotenuses match, and one other side matches. Right angle, hypotenuse, side is the RHS criterion.
  6. 2 · SAS needs two matching sides, plus the matching angle trapped between them.
  7. 60 · B matches E in the congruence statement, and corresponding angles of congruent triangles are equal, so angle E is 60 degrees.
  8. ASA · Two matching angles with the matching side between them is ASA: angle-side-angle.
  9. No, more than one triangle can fit these measurements · The 40 degree angle is opposite the 6 cm side, not between the two sides, so this is SSA. The 6 cm side can swing onto the 40 degree ray in two different places, so more than one triangle fits.
  10. 11 · The triangle inequality is strict: the third side must be shorter than 5 + 7 = 12 cm. The largest whole number below 12 is 11.
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