In ∆ABC and ∆DEF, ∠A ≅ ∠D and ∠B ≅ ∠E. What additional information is needed to prove that ∆ABC ≅ ∆DEF by the ASA Congruence Theorem?

Question

a. BC ≅ EF
b. AB ≅ DE
c. ∠C ≅ ∠F
d. AC ≅ DF

Answer 1

To use the ASA (Angle-Side-Angle) Congruence Theorem to prove that triangles ∆ABC and ∆DEF are congruent, we already have two pairs of angles that are congruent (∠A ≅ ∠D and ∠B ≅ ∠E).

We need one additional piece of information, specifically a side that is included between the two pairs of congruent angles. The side BC must be congruent to the side EF, or any side that corresponds with the established angles.

Therefore, the correct option is:

a. BC ≅ EF

This information allows us to establish that the triangles are congruent by the ASA theorem.