Question

What other information is needed to prove △ABC≅△QRS by ASA Congruence Theorem? (1 point) Responses AC¯¯¯¯¯¯¯¯≅QS¯¯¯¯¯¯¯ Modifying above upper A upper C with bar congruent to Modifying above upper Q upper S with bar ∠A≅∠Q angle upper A congruent to angle upper Q AB¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper Q upper R with bar ∠C≅∠S

Answer 1

To prove triangles △ABC and △QRS are congruent by the ASA (Angle-Side-Angle) Congruence Theorem, you need two angles and the side between them to be congruent in both triangles.

From your responses, you already have:
1. \( \angle A \cong \angle Q \)
2. \( AC \cong QS \) (this is the side between the angles).

Now, you also need the additional angle:
- \( \angle C \cong \angle S \) or \( \angle B \cong \angle R \) (one of these must be congruent to establish the second angle).

So, the complete information needed to prove △ABC ≅ △QRS by ASA is:
1. \( \angle A \cong \angle Q \) (one angle)
2. \( AC \cong QS \) (the side between the angles)
3. \( \angle C \cong \angle S \) (the second angle)

Thus, either of the last two (angle B with angle R, or angle C with angle S) is necessary depending on what is being compared.

The exact responses you need are:
- \( \angle C \cong \angle S \) to complete the proof by the ASA Criterion, assuming \( AC \) is the side between those angles.