Question

complete the congruence statement.
△fgh≅△

Explanation:

Step1: Match corresponding vertices

In congruent triangles, vertices are matched based on equal - side and equal - angle relationships. In \(\triangle FGH\) and the other triangle, \(\angle F = \angle N=90^{\circ}\), \(\angle G=\angle M = 45^{\circ}\), \(\angle H=\angle L = 45^{\circ}\), \(FG = MN = 34\) in, \(FH=LN = 34\) in, and \(GH = LM=49\) in.

Step2: Write congruence statement

The order of vertices in a congruence statement matters. Since \(F\) corresponds to \(N\), \(G\) corresponds to \(M\), and \(H\) corresponds to \(L\), the congruence statement is \(\triangle FGH\cong\triangle NML\).

Answer:

\(\triangle NML\)