Question

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

Answer 1

Proof : ∠ EFG = ∠FGH ..........  Alternate angles  (I)
∠ EFG = `1/2` [m(arc EG)] ........(Inscribed angle theorem) (II)

∠ FGH =`1/2` [m(arc FH)]  ........ (Inscribed angle theorem) (III)
∴ m(arc EG) = m(arc FH) ......... [(I), (II), (III) ]
∴ chord EG ≅ chord FH..... (corresponding chords of congruent arcs)