Triangle Congruence Worksheet

What does CPCTC stand for, and how is it used in geometry?

• Congruent Points Create Triangle Congruence; it is used to prove that two triangles are congruent.

• Corresponding Parts of Congruent Triangles are Congruent; it is used to prove that specific parts (angles or sides) of two congruent triangles are also congruent.

• Corresponding Points of Congruent Triangles are Congruent; it is used before proving triangle congruence.

• Congruent Parts Create Triangle Congruence; it is used to match triangles with similar shapes.

If △PQR is congruent to △STU, which of the following statements is false?

• ∠P = ∠S

• Side QR = Side TU

• Side PQ = Side ST

• ∠R = ∠T

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, which postulate proves the triangles are congruent?

• ASA

• AAS

• SAS

• SSS

In ΔABC and ΔDEF, AB ≅ DE, AC ≅ DF, and ∠A ≅ ∠D. What postulate can be used to prove ΔABC ≅ ΔDEF?

• AAS

• SAS

• ASA

• SSS

Which of the following combinations cannot be used to prove triangles congruent?

• SAS

• ASA

• SSS

• SSA

If ΔABC ≅ ΔDEF, which statement must be true?

• ∠B ≅ ∠F only

• ∠A ≅ ∠D and AB ≅ DE

• Only sides are congruent

• Angles are not congruent

Which information is enough to prove ΔABC ≅ ΔDEF by SAS?

• Two sides and a non-included angle

• Two sides and the included angle

• Three angles

• Two angles and one side

Given ΔABC with AB = 6 cm, BC = 8 cm, and ∠B = 45°, and ΔDEF with DE = 6 cm, EF = 8 cm, and ∠E = 45°, which triangles are congruent by which postulate?

• Yes, by SAS

• Yes, by ASA

• No, not enough information

• Yes, by AAS

If two right triangles have hypotenuses and one leg congruent, they are congruent by which theorem?

• ASA

• AAS

• HL

• SAS

Which condition is not necessary to use the HL Theorem?

• Both triangles are right triangles

• Hypotenuses are congruent

• One leg is congruent

• Both triangles are isosceles