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 .....$\boxed{\mathrm{property}\mathrm{of}\mathrm{alternate}\mathrm{angles}\mathrm{of}\mathrm{parallel}\mathrm{lines}}$ (I)

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

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

∴ m(arc EG) = $\boxed{m\left(\mathrm{arc}\mathrm{FH}\right)}$ from (I), (II), (III)

chord EG ≅ chord FH .....$\boxed{\mathrm{Chords}\mathrm{corresponding}\mathrm{to}\mathrm{congruent}\mathrm{arcs}\mathrm{of}\mathrm{a}\mathrm{circle}\mathrm{are}\mathrm{congruent}}$