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

(1 point)
Responses

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

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

1 answer

To determine whether the two triangles can be shown to be congruent using the Angle-Side-Angle (ASA) criterion, we need to confirm that:

  1. There are two angles and the included side in one triangle that correspond to two angles and the included side in the other triangle.

If you have measurements for two angles and the included side in both triangles, then you can indeed prove that they are congruent using ASA. If one of the triangles has a missing angle that can be calculated using the triangle angle sum theorem (which states that the sum of the angles in a triangle is 180 degrees), and this leads to two angles and the included side being congruent to those in the other triangle, you can also apply ASA.

Based on your options, the best answer seems to be:

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

This indicates that you can use ASA to show the triangles are congruent, assuming the provided angles and the side between them are relevant.