Question

In the adjoining figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.

Answer 1

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