Question

Three friends, Emma, Carol, and Mike are discussing the two triangles below. Emma says that they are congruent by applying the SAS rule, Carol disagrees and says that you need to apply the ASA rule, and Mike says that the triangles are not congruent. Who is correct?

Answer 1

Carol is right.

The segment shared by these two triangles is congruent to itself by the Reflexive Property, and so these two triangles are congruent by ASA.

Answer 2

Carol is right. The segment shared by these two triangles is congruent to itself by the Reflexive Property, and so these two triangles are congruent by ASA.

The triangles are mentioned as having a shared segment, which suggests that the side-angle-side (SAS) rule is applicable, not the angle-side-angle (ASA) rule. If the shared segment is a side and the corresponding angles are congruent, then Carol would be correct in stating that the triangles are congruent by the SAS rule.

Carol is right. The segment shared by these two triangles is congruent to itself by the Reflexive Property, and so these two triangles are congruent by ASA.