What other information is needed to prove triangle ABC cong triangle QRS Theorem? by ASA Congruence

Question

(1 point)

O overline AB cong overline QR

AC cong overline QS

O angle A cong angle Q

angle C cong angle S

Answer 1

To prove that triangle ABC is congruent to triangle QRS by ASA (Angle-Side-Angle) congruence, you need to establish two angles and the side between them as being congruent in both triangles.

From your provided information, you have:

1. \( \overline{AB} \cong \overline{QR} \) (one pair of sides)
2. \( AC \cong \overline{QS} \) (another pair of sides)
3. \( \angle A \cong \angle Q \) (one pair of angles)

For ASA congruence, you need:

• Two angles and the side between them are congruent.

You already have:

• \( \angle A \cong \angle Q \)
• You still need to establish that the side between them is congruent, and you need one more angle.

So, based on your options, you should have:

• \( \angle C \cong \angle S \)

This would be the information required to complete the congruence proof using ASA.

Thus, the additional needed statement would be:
\( \angle C \cong \angle S \).