Congruent Triangles and the Congruence Conditions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Proving triangles match exactly

Mathematics · Geometry · ages 14-15
Name ______________________   Date ____________

  1. Two right-angled triangles have matching hypotenuses of 10 cm and a matching side of 6 cm. Which condition matches?

    • SAS
    • ASA
    • RHS

  2. A diagram marks all three sides of triangle ABC equal to the three sides of triangle DEF. Which condition matches?

    • RHS
    • SSS
    • ASA

  3. Triangles ABC and DEF are congruent, with B matching E and C matching F. Side BC is 9 cm long. What is EF in cm?

    Answer: ______________

  4. A diagram marks AB equal to DE, BC equal to EF, and angle B equal to angle E. Which condition matches?

    • SAS
    • SSS
    • ASA

  5. Two right-angled triangles have matching hypotenuses of 13 cm and one matching side of 5 cm. Which condition matches?

    • SAS
    • SSS
    • RHS

  6. Triangles ABC and DEF are congruent. Side BC is 7 cm and side EF matches BC. What is EF in cm?

    Answer: ______________

  7. Triangles PQR and STU are congruent, with P matching S and Q matching T. Angle Q is 55 degrees. What is angle T in degrees?

    Answer: ______________

  8. Triangles PQR and STU are congruent, with Q matching T. Angle Q is 70 degrees. What is angle T in degrees?

    Answer: ______________

  9. A diagram gives two sides and a non-included angle matching. What can you conclude?

    • Congruent by SAS
    • Congruent by SSS
    • Nothing yet: this is not enough

  10. Triangles ABC and DEF are congruent. A congruence argument shows that side AB matches side DE. Side AB is 12 cm long. What is DE in cm?

    Answer: ______________

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Answer key

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

Proving triangles match exactly W1-mt_it8t7mY71J-s1

  1. RHS · Right angle plus matching hypotenuse and one side is RHS.
  2. SSS · Three matching sides is side-side-side.
  3. 9 · B matches E and C matches F, so side BC matches side EF. Congruent triangles have equal corresponding sides, so EF is 9 cm.
  4. SAS · Two sides with the angle between them is side-angle-side.
  5. RHS · A right angle plus matching hypotenuse and one other side is RHS.
  6. 7 · A congruence argument makes matching sides equal, so EF is 7.
  7. 55 · Q matches T, and matching angles of congruent triangles are equal, so angle T is 55 degrees.
  8. 70 · Matching angles of congruent triangles are equal, so T is 70.
  9. Nothing yet: this is not enough · The swinging side can land in two places, so congruence is unproved.
  10. 12 · The congruence argument pairs AB with DE, and matching sides of congruent triangles are equal, so DE is 12 cm.
Worksheet · LightMySky