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?

    • EF
    • DE
    • FD

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

    • SSS
    • ASA
    • RHS

  3. In triangle ABC, side a is the side opposite angle A.

    Circle one:   True   False

  4. 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

  5. A triangle has a right angle. Which criterion checks the hypotenuse and one other side to prove it congruent to another right triangle?

    • RHS
    • SAS
    • SSS

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

    • 1
    • 2
    • 3

  7. Zara says: triangle ABC and triangle DEF each have a 60 degree angle and their other two angles match too, so the triangles must be congruent. Is Zara correct?

    • No, matching angles alone do not guarantee congruence
    • Yes, matching all three angles is always enough
    • Yes, because 60 degrees is a right angle

  8. A triangle has sides 5 cm and 8 cm, and a 40 degree angle that is not between those two sides. Does this fix exactly one possible triangle?

    • No, more than one triangle can fit these measurements
    • Yes, exactly one triangle always fits
    • No, no triangle can be made
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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. SSS · When every side matches, that is SSS: side-side-side.
  3. True · The lowercase side letter sits opposite the matching capital vertex letter. That is the naming rule for triangle ABC.
  4. ASA · Two matching angles with the matching side between them is ASA: angle-side-angle.
  5. RHS · RHS stands for right angle, hypotenuse, side, and it only applies to right triangles.
  6. 2 · SAS needs two matching sides, plus the matching angle trapped between them.
  7. No, matching angles alone do not guarantee congruence · Matching angles only proves the triangles are the same shape. Without at least one matching side, the sizes could still differ, so they might not be congruent.
  8. No, more than one triangle can fit these measurements · When the angle is not the included angle, two different triangles can sometimes fit the same measurements. That is why side-side-angle is not a valid congruence test.
Worksheet · LightMySky