Question

complete the congruence statement.
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Explanation:

Step1: Identify corresponding vertices

In congruent triangles, vertices are listed in order of correspondence. In \(\triangle HGI\), vertex \(H\) is the right - angled vertex, \(G\) is the vertex with \(45^{\circ}\) angle, and \(I\) is the remaining vertex.

Step2: Determine the congruent triangle

Since the triangles are congruent (right - angled with two sides \(20\) ft and hypotenuse \(28\) ft and angles \(90^{\circ},45^{\circ},45^{\circ}\)), the corresponding triangle will have vertices in the same order. If we assume a triangle \(\triangle JKL\) (for example, but in standard naming based on the figure's structure, if we consider the right - angle, \(45^{\circ}\) angles and side lengths). The order of vertices for the congruent triangle: the right - angled vertex, the \(45^{\circ}\) angle vertex, and the other vertex. If we follow the naming convention (assuming no other figure labels, but based on the standard of congruence statements where we match angles and sides). Let's assume the other triangle (if we consider the order of right - angle (\(90^{\circ}\)), then \(45^{\circ}\), then \(45^{\circ}\)). The congruence statement \(\triangle HGI\cong\triangle IHG\) is wrong. Wait, no. Wait, in congruence of triangles, we can use the ASA (Angle - Side - Angle) or SAS (Side - Angle - Side) or SSS (Side - Side - Side) criteria. Here, we have a right - triangle (\(HL\) - Hypotenuse - Leg for right - triangles). But for the congruence statement, we match vertices. Since \(\angle H=\angle H = 90^{\circ}\), \(\angle G=\angle I = 45^{\circ}\), \(\angle I=\angle G=45^{\circ}\), \(HG = HI = 20\) ft, \(GI=IG = 28\) ft. The congruence statement is \(\triangle HGI\cong\triangle IHG\)

Answer:

\(\triangle IHG\)