Complete the following statement of congruence: ANOM = A. ARTS B. 4STR C. ATSR D. 4SRT Submit PREVIOUS
The Correct Answer and Explanation is:
The correct answer is A. ΔRTS.
To complete the statement of congruence, ΔNOM ≅ _____, we need to establish a correct correspondence between the vertices of the two triangles. The order of the vertices in the naming of a triangle is significant because it indicates which angles and sides are congruent.
First, let’s analyze the visual characteristics of the triangles. In triangle NOM, angle N is clearly an obtuse angle (greater than 90 degrees). In the other triangle, with vertices R, S, and T, angle R is the obtuse angle. Since corresponding parts of congruent triangles are congruent, the obtuse angle in one triangle must match the obtuse angle in the other. Therefore, vertex N corresponds to vertex R.
Next, we can compare the remaining vertices by looking at the side lengths. Let’s identify the shortest side in each triangle. In ΔNOM, the side opposite angle M is side NO. Visually, NO appears to be the shortest side of this triangle. In the second triangle, the side opposite angle S is side RT. Visually, RT appears to be the shortest side of its triangle. Because the shortest sides must correspond, side NO is congruent to side RT.
The vertices opposite these shortest sides must also correspond. In ΔNOM, vertex M is opposite side NO. In the other triangle, vertex S is opposite side RT. Therefore, vertex M corresponds to vertex S.
By process of elimination, we have one vertex left in each triangle. Vertex O in ΔNOM must correspond to vertex T in the other triangle.
We can now summarize the correspondences between the vertices:
- N corresponds to R
- O corresponds to T
- M corresponds to S
Using this established order, we can write the congruence statement. We match the sequence of vertices in ΔNOM with their corresponding partners. The first vertex N is matched with R. The second vertex O is matched with T. The third vertex M is matched with S. This gives us the name ΔRTS.
Therefore, the correct and complete statement of congruence is ΔNOM ≅ ΔRTS.
