In figure 3.95, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof. Proof : Draw seg GF. ∠ EFG = ∠ FGH ...Alternate interior angles....... (I) ∠ EFG = …………90° ………{inscribed angle theorem}(II) ∠ FGH = …………… 90° ………….{inscribed angle theorem} (III) ∴ m(arc EG) = ……………90°…………. from (I), (II), (III). chord EG ≅ chord FH ..........

Question

Philoid · Accepted Answer

Proof : Draw seg GF.

∠ EFG = ∠ FGH {Alternate interior angles} (I)

∠ EFG = 90°{inscribed angle theorem}(II)

∠ FGH = 90°{inscribed angle theorem} (III)

∴m(arc EG) = 90° from (I), (II), (III).

chord EG ≅ chord FH {Corresponding chords of congruent arcs of a circle (or congruent circles) are congruent}