The triangles TUV and VUT are congruent. This is supported by the congruence of side TU and VT, angle U and V, and the common side UV. The congruence postulate used is SAS (Side-Angle-Side).
1: List the parts of the triangles that are congruent. State how you know. If it is marked congruent in the diagram, write “congruent” in the space provided.
The congruent parts in the diagram are:
Side TU and Side VT: They are marked congruent in the diagram, so write “congruent” in the space provided.
Angle U and Angle V: They are marked congruent in the diagram, so write “congruent” in the space provided.
Side UV: It is the common side of both triangles, so it is congruent to itself by the reflexive property.
2: Name the congruence postulate that can be used to prove that the triangles are congruent.
The triangles are congruent by SAS (Side-Angle-Side) postulate. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
3: Write a congruence statement for the triangles.
A congruence statement for the triangles is Triangle TUV is congruent to Triangle VUT. This statement shows that the corresponding vertices of the triangles are in the same order.