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

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 shows two right-angled triangles with matching hypotenuses of 10 cm and a matching side of 6 cm. Which condition matches?

    • SSS
    • SAS
    • ASA
    • RHS

  3. Triangles ABC and DEF are congruent. The diagram marks BC = 7 cm. Side EF matches BC. What is EF in centimetres?

    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. A diagram marks angle A = angle D, angle B = angle E and side AB = side DE. Which condition matches?

    • SSS
    • SAS
    • ASA
    • SSA

  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, Q matching T and R matching U. Angle Q is 70°. 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. In a diagram, triangles ABC and DEF are congruent with A matching D. The diagram marks angle A = 48 degrees. A congruence argument justifies that angle D equals angle A. What is angle D in degrees?

    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. RHS · Right angle plus matching hypotenuse and one side is RHS.
  3. 7 · A congruence argument shows the matching sides are equal, so EF = 7 cm.
  4. SAS · Two sides with the angle between them is side-angle-side.
  5. ASA · Two angles with the side between them is angle-side-angle.
  6. 7 · A congruence argument makes matching sides equal, so EF is 7.
  7. 70 · Q pairs with T, so angle T equals angle Q: 70°.
  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. 48 · A pairs with D, so angle D = 48°.
Worksheet · LightMySky