Question

fi = ei and hi = gi. complete the proof that △ehi ≅ △fgi.

statement
1 fi = ei
2 hi = gi
3 ∠ehi = ∠fgi
4 △ehi ≅ △fgi

reason
given
given

Explanation:

Step1: Vertical angles

Vertical angles are equal. So, \(\angle EIH=\angle FIG\) because they are vertical angles.

Step2: SAS Congruence

We have \(FI = EI\) (given), \(\angle EIH=\angle FIG\) (vertical angles), and \(HI = GI\) (given). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle EIH\cong\triangle FIG\).

Answer:

1. \(FI = EI\) (Given)
2. \(HI = GI\) (Given)
3. \(\angle EIH=\angle FIG\) (Vertical angles are congruent)
4. \(\triangle EIH\cong\triangle FIG\) (SAS Congruence)