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Question

Two congruent triangles, upper A upper B upper C and upper Q upper R upper S are shown within an 11 column by 5 row grid. Angles upper B and upper R are marked congruent by double arcs. Sides upper B upper C and upper R upper S are labeled as 3 inches.

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

(1 point)
Responses

∠A≅∠Q
angle upper A congruent to angle upper Q

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

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

Answer 1

To prove that triangles \( \triangle ABC \) and \( \triangle QRS \) are congruent using the ASA (Angle-Side-Angle) Congruence Theorem, you need to establish that two angles and the included side of each triangle are congruent.

Since you already have:

• Angles \( \angle B \) and \( \angle R \) marked as congruent.
• Sides \( BC \) and \( RS \) marked as congruent (both are 3 inches).

Now, you need information about another angle in each triangle.

The options provided include:

1. \( \angle A \cong \angle Q \)
2. \( AC \cong QS \)
3. \( AB \cong QR \)
4. \( \angle C \cong \angle S \)

The correct option to provide the necessary information for proving \( \triangle ABC \cong \triangle QRS \) by ASA is:

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

This is because you need one additional angle to complete the set of angles for the ASA theorem—one angle from triangle \( ABC \) and the corresponding angle from triangle \( QRS \). Thus, the answer is:

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