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Omari wants to prove △ABC≅△QRS

by the ASA Congruence Theorem. What information is missing that would allow him to use this theorem?

(1 point)
Responses

∠B≅∠R
angle upper B congruent to angle upper R

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

BC¯¯¯¯¯¯¯¯≅RS¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper R upper S with bar

AB¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯

1 answer

To use the ASA (Angle-Side-Angle) Congruence Theorem, Omari needs to have two angles and the included side of one triangle congruent to the corresponding parts of the other triangle.

Given that Omari wants to prove \( \triangle ABC \cong \triangle QRS \) by ASA, he needs the following:

  1. Two pairs of angles (for example, \( \angle A \cong \angle Q \) and \( \angle B \cong \angle R \)).
  2. The side that is included between these two angles (for example, \( AB \cong QR \)).

Given the choices provided, one option among them will provide the necessary side congruence.

  • If he already has \( \angle A \cong \angle Q \), then to complete the ASA criteria, he needs either:
    • \( \angle B \cong \angle R \) (which is the congruence of the second angles) and the included side (which is \( AB \cong QR \) in this context),
    • or one of the other conditions listed to ensure the appropriate match.

However, without specific information about angles A and Q, we cannot determine which angle or side congruence is missing without the complete context provided with the initial premises.

If we assume that he only has one pair of angles established, the missing information could reasonably be:

  • \( AB \cong QR \) (which ensures the included side is congruent between the two triangles if the other angles are congruent as well).

So given the provided choices, if only one line is needed to prove ASA, the best response would be:
\( AB \cong QR \), as it indicates the side that is included between the two angles he wishes to prove congruent.