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 ∠C≅∠S angle upper C congruent to angle upper S AB¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯

Question

the image:
The image shows a coordinate plane with two triangles, ( \triangle ABC ) and ( \triangle QRS ), sharing a common vertex ( C ). Here are the details:

Vertices and Labels:
Triangle ( \triangle ABC ):
Vertex ( A ) is located at the bottom left.
Vertex ( B ) is at the top left.
Vertex ( C ) is at the center, shared with ( \triangle QRS ).
Triangle ( \triangle QRS ):
Vertex ( Q ) is at the bottom center.
Vertex ( R ) is at the top right.
Vertex ( S ) is at the bottom right.
Shared Side:
Both triangles share the side ( \overline{CQ} ).
Measurements:
The side ( \overline{BC} ) of ( \triangle ABC ) is labeled as 3 inches.
The side ( \overline{RS} ) of ( \triangle QRS ) is also labeled as 3 inches.
Grid and Units:
The coordinate plane is divided into a grid where each square represents one unit of measurement.
The triangles are drawn with orange lines, making them stand out against the grid. The shared side ( \overline{CQ} ) connects the two triangles, and the given measurements help in understanding the proportions and congruence between the triangles.

Answer 1

To prove that triangles \( \triangle ABC \) and \( \triangle QRS \) are congruent using the ASA (Angle-Side-Angle) Congruence Theorem, we need the following pieces of information:

1. We already have \( \angle A \cong \angle Q \) and the lengths of \( \overline{BC} \) and \( \overline{RS} \) are given as equal (3 inches). This serves as the side between the two angles.

2. We need to establish another pair of angles, specifically \( \angle C \) and \( \angle S \). If we can show that \( \angle C \cong \angle S \), we can proceed with the ASA proof.

Thus, the necessary information to prove \( \triangle ABC \cong \triangle QRS \) by the ASA Congruence Theorem would be to confirm:

• \( \angle C \cong \angle S \)

With this information, we have two pairs of angles ( \( \angle A \cong \angle Q \) and \( \angle C \cong \angle S \) ) and one included side ( \( \overline{BC} \cong \overline{RS} \)), satisfying the ASA condition for triangle congruence.