Questions: Complete the two-column proof Given: overline E congruent to overline GH, overline EF congruent to overline HF, F is the midpoint of overline GI Prove: triangle EFI congruent to triangle HFG Statements Reasons 1) overline IE congruent to overline GH, overline EF congruent to overline HF

Complete the two-column proof
Given: overline E congruent to overline GH, overline EF congruent to overline HF, F is the midpoint of overline GI
Prove: triangle EFI congruent to triangle HFG

Statements
Reasons
1) overline IE congruent to overline GH, overline EF congruent to overline HF
Transcript text: Complete the two-column proof Given: $\overline{\mathrm{E}} \cong \overline{\mathrm{GH}}, \overline{\mathrm{EF}} \cong \overline{\mathrm{HF}}$, F is the midpoint of $\overline{\mathrm{GI}}$ Prove: $\triangle E F I \cong \triangle H F G$ Statements Reasons 1) $\overline{\mathrm{IE}} \cong \overline{\mathrm{GH}}, \overline{\mathrm{EF}} \cong \overline{\mathrm{HF}}$
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Solution

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Solution Steps

Step 1: Given Information

Statements:

  1. \( IE \cong GH \), \( EF \cong HF \)

Reasons:

  1. Given
Step 2: Midpoint Definition

Statements: 2. \( F \) is the midpoint of \( GI \)

Reasons: 2. Given

Step 3: Segment Congruence

Statements: 3. \( GF \cong IF \)

Reasons: 3. Definition of midpoint

Step 4: Triangle Congruence

Statements: 4. \( \triangle EFI \cong \triangle HFG \)

Reasons: 4. Side-Side-Side (SSS) Congruence Postulate

Final Answer

The triangles \( \triangle EFI \) and \( \triangle HFG \) are congruent by the SSS Congruence Postulate.

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