Question

given statement
fg ≅ he
diagram
yes/no?
is enough information given in the figure to show that the given statement is true?

Explanation:

Step1: Analyze triangles \( \triangle HEF \) and \( \triangle HGF \)

In \( \triangle HEF \) and \( \triangle HGF \), we have \( \angle EHF=\angle GHF \) (given angle), \( \angle EFH = \angle GFH \) (given angle), and \( HF = HF \) (common side).

Step2: Use AAS (Angle - Angle - Side) congruence criterion

By the AAS congruence criterion, \( \triangle HEF\cong\triangle HGF \).

Step3: Conclude the side - length relationship

Since \( \triangle HEF\cong\triangle HGF \), then \( FG = HE \) (corresponding parts of congruent triangles are equal).

Answer:

Yes