Given: E is the midpoint of HF and GK

Prove: HK = GF

SAS (Side-Angle-Side)
CPCTC
<HEK = <FEG
E is the midpoint of HF and GK
HK = GF
Given
Definition
HE = FE and KE = GE
Definition
Triangle HEK = Triangle FEG
<HEK and <FEG are vertical angles
Vertical angles are equal