Question

if de = dg = 51 and fg = 80, what is ef?
ef =

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \(DE = DG = 51\) and \(FD\) is a common side (\(FD = FD\)) and \(\angle FDG=\angle FDE = 90^{\circ}\), by the HL (Hypotenuse - Leg) Congruence Theorem, \(\triangle FDG\cong\triangle FDE\).

Step2: Use the property of congruent triangles

If \(\triangle FDG\cong\triangle FDE\), then their corresponding sides are equal. So \(FG = EF\).

Answer:

\(80\)