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

(1 point)
Responses
tell me the correct answer by solving it and tell me why
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
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

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

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

To determine if the two triangles can be shown to be congruent using the Angle-Side-Angle (ASA) postulate, we need to analyze the given information.

The ASA postulate states that if two angles and the included side (the side between the two angles) of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

From your question, we need to consider the following:

  1. Angle Measurements: We need two angles from each triangle.
  2. Included Side: We need the side between those two angles to be equal.

If you have two angle measurements for each triangle and confirm that the included side between those angles is also equal, you can use ASA to show that the two triangles are congruent.

Given your responses, the most appropriate answer seems to be:

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

This means that if the angles and the included side are the same in both triangles, you can conclude that the triangles are congruent using the ASA postulate.

The first option about using the triangle angle sum theorem to find a missing angle is not directly related to ASA unless you can explicitly match the angles and their included sides. Therefore, it’s better to stick with the direct response regarding the given properties.