{"id":241683,"date":"2025-07-03T19:45:36","date_gmt":"2025-07-03T19:45:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=241683"},"modified":"2025-07-03T19:45:38","modified_gmt":"2025-07-03T19:45:38","slug":"complete-the-following-statement-of-congruence","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/complete-the-following-statement-of-congruence\/","title":{"rendered":"Complete the following statement of congruence"},"content":{"rendered":"\n

Complete the following statement of congruence: ANOM = A. ARTS B. 4STR C. ATSR D. 4SRT Submit PREVIOUS<\/p>\n\n\n\n

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The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is A. \u0394RTS<\/strong>.<\/p>\n\n\n\n

To complete the statement of congruence, \u0394NOM \u2245 _____, 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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Next, we can compare the remaining vertices by looking at the side lengths. Let\u2019s identify the shortest side in each triangle. In \u0394NOM, 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.<\/p>\n\n\n\n

The vertices opposite these shortest sides must also correspond. In \u0394NOM, vertex M is opposite side NO. In the other triangle, vertex S is opposite side RT. Therefore, vertex M corresponds to vertex S.<\/p>\n\n\n\n

By process of elimination, we have one vertex left in each triangle. Vertex O in \u0394NOM must correspond to vertex T in the other triangle.<\/p>\n\n\n\n

We can now summarize the correspondences between the vertices:<\/p>\n\n\n\n