Question

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

Answer 1

Proof: Draw seg GF.

∠EFG = ​∠FGH .....property of alternate angles of parallel lines      (I)

∠EFG = ​ \[\frac{1}{2}m\left( arc EG \right)\]         .....inscribed angle theorem (II)

∠FGH = ​ \[\frac{1}{2}m\left( arc FH \right)\]       .....inscribed angle theorem (III)

∴ m(arc EG) = \[m\left( arc FH \right)\]        from (I), (II), (III)

chord EG ≅ chord FH        ....  Chords corresponding to congruent arcs of a circle are congruent.