Question

name: ____________________________ date: ____________________

1. given: ( overline{ie} cong overline{gh} ), ( overline{ef} cong overline{hf} ),

( f ) is the midpoint of ( overline{gi} )
prove: ( \triangle efi cong \triangle hfg )

statements	reasons
2)	2)
3)	3)

Explanation:

Step1: Identify Given Information

We are given that \( \overline{IE} \cong \overline{GH} \), \( \overline{EF} \cong \overline{HF} \), and \( F \) is the midpoint of \( \overline{GI} \). By the definition of a midpoint, if \( F \) is the midpoint of \( \overline{GI} \), then \( \overline{FI} \cong \overline{FG} \).

Step2: List Statements and Reasons

1. Statement 1: \( \overline{IE} \cong \overline{GH} \), \( \overline{EF} \cong \overline{HF} \), \( F \) is the midpoint of \( \overline{GI} \)

Reason 1: Given

1. Statement 2: \( \overline{FI} \cong \overline{FG} \)

Reason 2: Definition of a midpoint (a midpoint divides a segment into two congruent segments)

1. Statement 3: \( \triangle EFI \cong \triangle HFG \)

Reason 3: SSS (Side - Side - Side) Congruence Postulate (since we have three pairs of congruent sides: \( \overline{IE} \cong \overline{GH} \), \( \overline{EF} \cong \overline{HF} \), and \( \overline{FI} \cong \overline{FG} \))

Answer:

Statements	Reasons
2. \( \overline{FI} \cong \overline{FG} \)	2. Definition of midpoint
3. \( \triangle EFI \cong \triangle HFG \)	3. SSS Congruence Postulate