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 AB¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper Q upper R with bar ∠A≅∠Q angle upper A congruent to angle upper Q ∠C≅∠S

Answer 1

To prove that triangle \( \triangle ABC \) is congruent to triangle \( \triangle QRS \) using the ASA (Angle-Side-Angle) Congruence Theorem, you need the following information:

1. **Two angles** of one triangle must be congruent to two angles of the other triangle.
- You already have \( \angle A \cong \angle Q \) (as you indicated), and you need one more angle.
- You can state \( \angle C \cong \angle S \) (from your options).

2. **The side between the two angles** must also be congruent.
- To fulfill the ASA condition, you will need \( AC \cong QS \) (or whatever side is corresponding).

Putting this together, the information needed to complete the proof is:

1. \( \angle A \cong \angle Q \)
2. \( \angle C \cong \angle S \)
3. The side \( AC \cong QS \) (or \( AB \cong QR \) if you were using \( AB \) as the corresponding side).

With these angles and the included side, you will have everything needed to apply the ASA Congruence Theorem.