Worksheet: Conditions for Triangle Congruence

In this worksheet, we will practice identifying congruent triangles by applying SSS, SAS, and ASA criteria.


The shape 𝐴 𝐵 𝐹 𝐶 in the given figure is a parallelogram.

What can be said of the lengths of 𝐴 𝐶 and 𝐵 𝐹 ?

  • AThey are equal.
  • BThey are different.

Which angle has the same measure as 𝐴 𝐶 𝐸 ?

  • A 𝐸 𝐵 𝐹
  • B 𝐴 𝐸 𝐶
  • C 𝐸 𝐶 𝐹
  • D 𝐶 𝐴 𝐸
  • E 𝐶 𝐸 𝐹

Which angle has the same measure as 𝐶 𝐴 𝐸 ?

  • A 𝐴 𝐸 𝐵
  • B 𝐸 𝐵 𝐹
  • C 𝐸 𝐹 𝐵
  • D 𝐴 𝐶 𝐸
  • E 𝐴 𝐸 𝐶

Given the information gained from the previous sections and the 𝐴 𝑆 𝐴 congruence criterion, are triangles 𝐴 𝐶 𝐸 and 𝐹 𝐸 𝐵 congruent?

  • ANo
  • BYes


State whether the figures are congruent or not congruent.

  • Anot congruent
  • Bcongruent


Each of 32 students in a class have three straws with lengths of 3 inches, 4 inches, and 6 inches, with which they make a triangle. What would be true of all the triangles that they make?

  • A They would all be isosceles.
  • B They would all be equilateral.
  • C They would all be acute triangles.
  • D They would all be congruent.
  • E They would all be right triangles.


The diagonal of the rectangle divides its surface into two triangles.

  • A congruent
  • B different


In the figure, 𝐴 𝐵 𝐷 𝐸 .

Which congruence criterion could be used to prove the two triangles are congruent?

  • A The SAS rule will prove congruence.
  • B The AAS rule will prove congruence.
  • C The ASA rule will prove congruence.
  • DThere is not enough information to prove congruence.
  • E The AAA rule will prove congruence.


In the given figure, 𝐴 𝐵 is the perpendicular bisector of 𝐶 𝐷 . By definition, 𝐶 𝐸 is equal to 𝐸 𝐷 , 𝐴 𝐸 is a common side to both angles, and 𝐴 𝐸 𝐶 and 𝐴 𝐸 𝐷 are both right angles.

Which congruence criterion could be used to prove that triangle 𝐴 𝐸 𝐶 and triangle 𝐴 𝐸 𝐷 are congruent?

  • A ASA
  • B SSS
  • C SAS

As triangle 𝐴 𝐸 𝐶 and triangle 𝐴 𝐸 𝐷 are congruent, determine what will be true of the line segments 𝐴 𝐶 and 𝐴 𝐷 , wherever 𝐴 may lie on the line.

  • AThey will be congruent.
  • BThey will be parallel.
  • CThey will be perpendicular.


Complete the sentence: These figures are .

  • Asimilar but not congruent
  • Bneither similar nor congruent
  • Ccongruent


The two triangles in the given figure have equal sides. Are the two triangles congruent?

  • A yes
  • B no

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