What other information is needed to

Question

prove AABC = AQRS by ASA
Congruence Theorem?
(1 point)
O ABE QR
OLAE<Q
OLCELS
O ACE QS

Answer 1

To prove that triangle $AABC$ is congruent to triangle $AQRS$ by the ASA (Angle-Side-Angle) Congruence Theorem, you need the measures of two angles and the length of the side that is included between those two angles for both triangles.

Among the options provided:

• $\mathrm{\angle }ABE\equiv \mathrm{\angle }QR$: This option states that an angle in triangle $AABC$ is congruent to an angle in triangle $AQRS$.
• $\mathrm{\angle }A<\mathrm{\angle }Q$: This option is about inequality and does not help with congruence.
• $\mathrm{\angle }CEL\equiv \mathrm{\angle }S$: This option states the congruence of another pair of angles.
• $\mathrm{\angle }ACE\equiv \mathrm{\angle }QS$: This option states another angle congruence.

To utilize the ASA congruence theorem effectively, you need:

1. Two angles from both triangles that are congruent.
2. The side that is included between those two angles in both triangles must also be congruent.

However, based on the given options, the congruence of the angles between the two triangles must indeed involve a specific included side being congruent. Therefore, for the ASA criterion, if you need to select the most appropriate option, it should include both the congruence of two angles and the length of the side between those angles.

Since none of the options clearly state an included side being equal, the correct approach cannot be determined without further context about which angles correspond to which sides.

To conclude, you require two angles that are congruent and the corresponding side included between them as congruent in both triangles for the ASA theorem to apply. Make sure to check if there is information about side lengths in the context of your question, which is essential for the ASA criterion.