Given: E is the midpoint of HF and GK

Prove: HK = GF

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