Question

complete the congruence statement.

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Explanation:

Step1: Identify corresponding angles and sides

In congruent triangles, corresponding angles and sides are equal. In \(\triangle EDF\), \(\angle E = 90^{\circ}\), \(\angle D=45^{\circ}\), \(\angle F = 45^{\circ}\), \(ED = 28\) yd, \(EF = 28\) yd, \(FD=40\) yd.

Step2: Determine the congruent triangle

We need to match the vertices. Since the order of congruence matters (corresponding parts), and looking at the structure of the triangle (right - angled with two \(45^{\circ}\) angles and side lengths \(28\) yd and \(40\) yd), if we consider the right - angle vertex, side - side - angle (in the case of right - angled triangles, we can use the properties of congruence for right - angled triangles). The triangle \(\triangle FED\) has \(\angle FED = 90^{\circ}\), \(\angle EFD=45^{\circ}\), \(\angle EDF = 45^{\circ}\), \(FE = 28\) yd, \(ED = 28\) yd, \(FD = 40\) yd.

Answer:

\(\triangle FED\)