Question

What other information is needed to prove △ABC≅△QRS by ASA Congruence Theorem?

(1 point)
Responses

AB¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯
Modifying above upper A upper B with bar congruent to Modifying above upper Q upper R with bar

∠C≅∠S
angle upper C congruent to angle upper S

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

Answer 1

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

Given the options:

1. **AB ≅ QR**
2. **∠C ≅ ∠S**
3. **AC ≅ QS**
4. **∠A ≅ ∠Q**

To apply the ASA theorem, you need to show two angles and the side that is between them.

- If you already have the congruence of **∠A ≅ ∠Q** (first angle) and **∠C ≅ ∠S** (second angle), you would need to show that the included side **AC** is congruent to **QS** (the side between the two angles).

Thus, the essential information needed would be:

**AC ≅ QS**

This provides the necessary third congruence to use the ASA theorem.

So, if you are asked for the additional necessary information to prove the congruence based on the ASA theorem, the correct response would be:

**AC ≅ QS**