Question
What other information is needed to prove that △ABC ≅ △ QRS by ASA Congruence Theorem? (1 point) Responses AC¯¯¯¯¯¯¯¯ ≅ QS¯¯¯¯¯¯¯ AC¯¯¯¯¯¯¯¯ ≅ QS¯¯¯¯¯¯¯ ∠C ≅ ∠S ∠C ≅ ∠S AB¯¯¯¯¯¯¯¯ ≅ QR¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯ ≅ QR¯¯¯¯¯¯¯¯ BC¯¯¯¯¯¯¯¯ ≅ RS¯¯¯¯¯¯¯
Answers
GPT-4o mini
To prove that triangles \( \triangle ABC \) and \( \triangle QRS \) are congruent by the Angle-Side-Angle (ASA) Congruence Theorem, you need the following information:
- You must have one pair of corresponding angles that are congruent.
- The length of the side that is included between those angles must be congruent.
- You need one more pair of corresponding angles to be congruent.
From your options, you have:
1. If \( \angle C \cong \angle S \) (one pair of congruent angles).
2. A side included between those angles: either \( AC \cong QS \) or \( AB \cong QR \).
3. A second pair of angles: \( \angle A \cong \angle Q \) or \( \angle B \cong \angle R \) (this would provide the second congruent angle required for the ASA).
To succinctly state which specific additional information would complete the requirement:
- If you confirm \( \angle A \cong \angle Q \) (or another corresponding angle) along with one of the congruent sides (like \( AC \cong QS \)), then you would have everything needed for ASA.
Thus, any response indicating a congruent angle or a congruent side paired with the congruent angle should be chosen.
- You must have one pair of corresponding angles that are congruent.
- The length of the side that is included between those angles must be congruent.
- You need one more pair of corresponding angles to be congruent.
From your options, you have:
1. If \( \angle C \cong \angle S \) (one pair of congruent angles).
2. A side included between those angles: either \( AC \cong QS \) or \( AB \cong QR \).
3. A second pair of angles: \( \angle A \cong \angle Q \) or \( \angle B \cong \angle R \) (this would provide the second congruent angle required for the ASA).
To succinctly state which specific additional information would complete the requirement:
- If you confirm \( \angle A \cong \angle Q \) (or another corresponding angle) along with one of the congruent sides (like \( AC \cong QS \)), then you would have everything needed for ASA.
Thus, any response indicating a congruent angle or a congruent side paired with the congruent angle should be chosen.