Question

Date
E
Activity 12
In the figure, chord EF
chord GH. Prove that,
chord EG chord FH.
Complete the following
activity to write the proof.
Construction : Draw seg GF.
G
Proof: ZEFG = ZFGH​

Answer 1

Given: chord EF || chord GH 

To prove: chord EG = chord FH

Construction: Draw seg GF

Proof:  ∠EFG = ∠FGH (i)

Alternate angles ∠EFG = 1/2 m (arcEG)]

(ii) [Inscribed angle theorem]  ∠FGH = 1/2 m(arcFH) (iii) [Inscribed angle theorem]  ∴ m(arcEG) = m (are FH)

[From (i), (ii) and (iii)] 

∴ chord EG ≅ chord FH The chords corresponding to congruent arcs of a circle