In the Given Figure, Chord Ef || Chord Gh. Prove That, Chord Eg ≅ Chord Fh. Fill in the Blanks and Write the Proof. - Geometry Mathematics 2

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Sum

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

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Solution

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.
  Is there an error in this question or solution?
Chapter 3: Circle - Problem Set 3 [Page 88]

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