Complete the following statement of congruence
The Correct Answer and Explanation is:
The correct answer is B. ΔACB.
Explanation
To complete the statement of congruence, ΔXZY ≅ _____, we must identify the corresponding vertices of the two triangles in the correct order. Congruent triangles have identical corresponding sides and angles. The order of the vertices in a congruence statement indicates which parts correspond to each other.
Let’s analyze the two triangles, ΔXZY and ΔABC, to find the matching vertices.
- Identify Corresponding Angles:
- First, we can observe the right angles. In ΔXZY, the right angle is at vertex X. In the other triangle, the right angle is at vertex A. Therefore, vertex X corresponds to vertex A.
- Next, let’s look at the other vertices based on their positions. Vertex Z is at the top of the vertical side of ΔXZY. In the second triangle, vertex C is in the equivalent position, at the top of its vertical side. This means vertex Z corresponds to vertex C.
- Finally, vertex Y is at the end of the horizontal side, opposite the vertical side. In the second triangle, vertex B is in the same relative position. Thus, vertex Y corresponds to vertex B.
- Construct the Congruence Statement:
The problem asks for a triangle congruent to ΔXZY. We must list the corresponding vertices of the second triangle in the same sequence as X, Z, and Y.- The first vertex, X, corresponds to A.
- The second vertex, Z, corresponds to C.
- The third vertex, Y, corresponds to B.
Therefore, the complete and correct statement of congruence is ΔXZY ≅ ΔACB. This statement correctly implies that all corresponding parts are congruent: ∠X ≅ ∠A, ∠Z ≅ ∠C, ∠Y ≅ ∠B, and side XZ ≅ side AC, side ZY ≅ side CB, and side YX ≅ side BA. Option B is the only choice that reflects this proper correspondence
