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Question

Question
In order to prove that △ABC≅△QRS
using ASA, what OTHER information is needed?

(1 point)
Responses listen and be honest

∠A≅∠Q
∠A≅∠Q

∠C≅∠S
∠C≅∠S

AC¯¯¯¯¯¯¯¯≅ QS¯¯¯¯¯¯¯
AC¯¯¯¯¯¯¯¯≅ QS¯¯¯¯¯¯¯

AC¯¯¯¯¯¯¯¯≅ QS¯¯¯¯¯¯¯
AC¯¯¯¯¯¯¯¯≅ QS¯¯¯¯¯¯¯
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Answer 1

To prove that triangles \( \triangle ABC \cong \triangle QRS \) using the Angle-Side-Angle (ASA) criterion, you need to know two angles and the included side.

Given the options presented:

1. \( \angle A \cong \angle Q \)
2. \( \angle C \cong \angle S \)
3. \( \overline{AC} \cong \overline{QS} \)

You need two angles and the side between them (the included side).

If you already know one of the angles and the side, you would need another angle:

• If you have \( \angle A \cong \angle Q \) and you need \( \angle C \cong \angle S \), that could be sufficient if \( \overline{AC} \cong \overline{QS} \) is also true.
• The correct information to prove \( \triangle ABC \cong \triangle QRS \) using ASA should include:
  • One pair of angles (e.g., \( \angle A \cong \angle Q \))
  • The included side (e.g., \( \overline{AC} \cong \overline{QS} \))
  • And the second pair of angles (e.g., \( \angle C \cong \angle S \))

Based on the requirement of the ASA criterion, the best choice from the options would be:

\(\angle A \cong \angle Q\)

as you would also need to know another angle or the included side to finalize the proof. Depending on your specific context or what you already have, any of those three could potentially fulfill the need, so further context is key.