Question

if m∠efh = m∠gfh = 50° and eh = 51, what is gh? gh = work it out not feeling ready yet? these can help: submit

Explanation:

Step1: Identify the triangles

We have two right triangles, \(\triangle FEH\) and \(\triangle FGH\), with \(\angle FEH = \angle FGH = 90^\circ\), \(\angle EFH=\angle GFH = 50^\circ\), and \(FH\) is common to both triangles.

Step2: Prove triangle congruence

By the Angle - Angle - Side (AAS) congruence criterion, \(\triangle FEH\cong\triangle FGH\) because:

• \(\angle FEH=\angle FGH = 90^\circ\)
• \(\angle EFH=\angle GFH = 50^\circ\)
• \(FH = FH\) (common side)

Step3: Use congruence property

Since \(\triangle FEH\cong\triangle FGH\), their corresponding sides are equal. We know that \(EH = 51\), and the corresponding side of \(EH\) in \(\triangle FGH\) is \(GH\). So, \(GH=EH\).

Answer:

\(51\)