Final answer:
To prove that triangles ∆FEG and ∆HIG are congruent given that segments EI and FH are congruent and G is the midpoint of both, we use a two-column proof involving the SAS postulate.
Step-by-step explanation:
To prove that ∆FEG ≅ ∆HIG given that segment EI ≅ segment FH and point G is the midpoint of both segment EI and segment FH, we can construct a two-column proof using geometric congruence theorems such as the Side-Angle-Side postulate
Given: Segment EI ≅ Segment FH and G is the midpoint of both segments EI and FH.
Prove: ∆FEG ≅ ∆HIG.
Two-Column Proof
Statement Reason
1. Segment EI ≅ Segment FH Given
2. Point G is the midpoint of Segment EI and of Segment FH Given
3. Segment EG ≅ Segment HG and Segment FG ≅ Segment IG Definition of a midpoint
4. Angle EGF ≅ Angle HGI Vertical Angles are Congruent
5. ∆FEG ≅ ∆HIG SAS Postulate
By the Side-Angle-Side (SAS) postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Hence, we have proved that ∆FEG is congruent to ∆HIG.