Can the two triangles below be shown to be congruent using ASA?

Question

(1 point)
Responses

No, they can not be shown congrent with ASA
No, they can not be shown congrent with ASA

Yes, because there are 2 angle measurements given in each triangle and 1 side
Yes, because there are 2 angle measurements given in each triangle and 1 side

Yes, by using the triangle angle sum theorem, we can figure out that the missing angle in the pink triangle is 100 degrees and then use ASA

Answer 1

To determine if the two triangles can be shown to be congruent using ASA (Angle-Side-Angle), we need to verify the requirements:

1. Two Angles: We need to show that we have two pairs of angles in each triangle that are congruent.
2. Included Side: We need to show that the side between these two angles is congruent.

From the provided responses, the third response is the most complete. If you can find two angles in one triangle that are congruent to two angles in the other triangle, and you can determine the measure of the third angle using the triangle angle sum theorem (which states that the sum of the angles in a triangle is 180 degrees), then that would imply both triangles are congruent using ASA.

Thus, the correct reasoning would be:

• If we find that the missing angle in the pink triangle is indeed congruent to an angle in the other triangle (because we calculated it based on the other known angles), and we know the included side between those angles is congruent as well, then we can conclude that the triangles are congruent by ASA.

So, the best response is:

Yes, by using the triangle angle sum theorem, we can figure out that the missing angle in the pink triangle is 100 degrees and then use ASA.