Question

Which of the following statements is true?

1) The triangles are congruent by the ASA Congruence Postulate.
2) The triangles are congruent by the SAS Congruence Postulate
3) The triangles are congruent by the SSS Congruence Postulate
4) The triangles are congruent by the AAS congruence theorem

Answer 1

The correct statement is that the triangles are congruent by the ASA Congruence Postulate. ASA stands for Angle-Side-Angle. According to the ASA Congruence Postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Option number 1 is correct.

Step-by-step explanation:

The correct statement is:

1. The triangles are congruent by the ASA Congruence Postulate.

ASA stands for Angle-Side-Angle. According to the ASA Congruence Postulate, if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. In this case, the given information implies that the triangles have two congruent angles (since the side included between them is congruent) and one congruent side. Therefore, the triangles are congruent by the ASA Congruence Postulate.