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.

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

Answer 1

To prove that \( \triangle ABC \cong \triangle QRS \) by the ASA (Angle-Side-Angle) Congruence Theorem, we need two angles and the side that is included between those angles to be congruent in both triangles.

Given that \( \angle B \cong \angle R \) (marked by double arcs) and \( BC \cong RS \) (both sides labeled as 3 inches), we need one more angle.

Thus, any of the following options could suffice in different scenarios, but the most direct response given the angle data is:

• \( \angle A \cong \angle Q \)

This choice provides the second angle needed to apply the ASA congruence theorem along with the side \( BC \).

So, the answer is:

∠A≅∠Q (angle A congruent to angle Q)