In △ABC and △DEF , ∠A ≅ ∠D and ∠B ≅ ∠E What additional information is needed to prove that △ABC ≅ △DEF by the ASA Congruence Theorem? (1 point)

Question

In △ABC and △DEF , ∠A ≅ ∠D and ∠B ≅ ∠E What additional information is needed to prove that △ABC ≅ △DEF  by the ASA Congruence Theorem? (1 point)

GPT-4o mini · Answer

To prove that triangle $ \triangle ABC $ is congruent to triangle $ \triangle DEF $ by the ASA (Angle-Side-Angle) Congruence Theorem, you would need to know the lengths of one corresponding side of both triangles. Specifically, you can choose one of the sides that is included between the two pairs of congruent angles. For example, you can have either: - The length of side $ AB $ and $ DE $ (sides between angles $ A $ and $ B $ in $ \triangle ABC $ and angles $ D $ and $ E $ in $ \triangle DEF $), or - The length of side $ BC $ and $ EF $ (sides between angles $ B $ and $ C $ in $ \triangle ABC $ and angles $ E $ and $ F $ in $ \triangle DEF $), or - The length of side $ AC $ and $ DF $ (sides between angles $ A $ and $ C $ in $ \triangle ABC $ and angles $ D $ and $ F $ in $ \triangle DEF $). This additional information (the length of one corresponding side) is necessary to apply the ASA theorem for proving the congruence of the triangles.