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Lesson: Conditions for Triangle Congruence

Worksheet • 6 Questions


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

  • A different
  • B congruent


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


The shape 𝐴 𝐡 𝐹 𝐢 in the given figure is a parallelogram.

What can be said of the lengths of 𝐴 𝐢 and 𝐡 𝐹 ?

  • AThey are different.
  • BThey are equal.

Which angle has the same measure as ∠ 𝐴 𝐢 𝐸 ?

  • A ∠ 𝐸 𝐡 𝐹
  • B ∠ 𝐢 𝐸 𝐹
  • C ∠ 𝐢 𝐴 𝐸
  • D ∠ 𝐴 𝐸 𝐢
  • E ∠ 𝐸 𝐢 𝐹

Which angle has the same measure as ∠ 𝐢 𝐴 𝐸 ?

  • A ∠ 𝐸 𝐹 𝐡
  • B ∠ 𝐴 𝐸 𝐡
  • C ∠ 𝐸 𝐡 𝐹
  • D ∠ 𝐴 𝐸 𝐢
  • E ∠ 𝐴 𝐢 𝐸

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

  • Ano
  • Byes


In the figure, .

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

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


In the given figure, βƒ–     βƒ— 𝐴 𝐡 is the perpendicular bisector of 𝐢 𝐷 . By definition, 𝐢 𝐸 is equal to 𝐸 𝐷 , 𝐴 𝐸 is a common side to both angles, and ∠ 𝐴 𝐸 𝐢 and ∠ 𝐴 𝐸 𝐷 are both right angles.

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

  • A SSS
  • B SAS
  • C ASA

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

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


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

  • A no
  • B yes