Which triangles are congruent by SAS?
ABC and TUV
VTU and ABC
VTU and HGF
none of the above
None of the above.
Triangles ABC and TUV are congruent by SAS.
To determine which triangles are congruent by Side-Angle-Side (SAS) congruence, we need to compare and analyze the sides and angles of the given triangles.
SAS congruence states that if two triangles have two sides that are congruent and the included angle between these sides is congruent, then the two triangles are congruent.
Let's examine the given options:
1. ABC and TUV: We don't have any information about the included angle between the congruent sides. Therefore, we cannot determine the congruence of these triangles by SAS. This option can be eliminated.
2. VTU and ABC: Once again, we don't have information about the included angle between the congruent sides. Therefore, we cannot determine the congruence of these triangles by SAS. This option can be eliminated.
3. VTU and HGF: Since there is no mention of congruent sides or angles, we cannot determine the congruence of these triangles by SAS. This option can be eliminated.
From the given options, none of the triangles are congruent by SAS. Therefore, the correct answer is "none of the above."