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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

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

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

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

AC¯¯¯¯¯¯¯¯≅QS¯¯¯¯¯¯¯

Answer 1

To prove that triangles \( \triangle ABC \) and \( \triangle QRS \) are congruent by the ASA (Angle-Side-Angle) Congruence Theorem, we need two angles and the included side to be congruent. We already know that \( \angle B \cong \angle R \) and that the sides \( BC \) and \( RS \) are congruent (both are 3 inches).

Thus, we need one more angle congruence to apply ASA. Among the options provided, either \( \angle A \cong \angle Q \) or \( \angle C \cong \angle S \) would suffice, but we only need one of them.

The most suitable response to provide the necessary information to apply the ASA theorem would be:

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

This shows that we have two angles \( \angle A \) and \( \angle B \) from triangle \( ABC \) congruent to angles \( \angle Q \) and \( \angle R \) from triangle \( QRS \), and the included side \( BC \) is also congruent to side \( RS \).