Given: chord EF || chord GH
To prove: chord EG = chord FH
Construction: Draw seg GF
Proof:
∠EFG = ∠FGH (i) Alternate angles
∠EFG = 1/2 m (arcEG)] (ii) [Inscribed angle theorem]
∠FGH = 1/2 m(arcFH) (iii) [Inscribed angle theorem]
∴ m(arcEG) = m (are FH) [From (i), (ii) and (iii)]
∴ chord EG ≅ chord FH The chords corresponding to congruent arcs of a circle are congruent