Question

If chord EF parallel to Chord GH.Prove that chord EG congruent to chord FH

Answer 1

EG = FH (Proved)

Step-by-step explanation:

See the attached diagram.

Take triangles Δ EFG and Δ EFH,

(i) ∠ EGF = ∠ EHF

{Because they are angles of the same circle subtended by the same chord EF}

(ii) ∠ EFG = ∠ FEH

Since ∠ FEH = ∠ FGH as they are angles of the same circle subtended by the same chord FH.

Again, ∠ EFG = ∠ FGH, since EF║ GH and FG is the transverse line. (Alternate angles)

So, ∠ EFG = ∠ FEH.

(iii) EF is the common side.

So, by AAS criteria Δ EFG ≅ Δ EFH.

Hence, EG = FH {Corresponding Sides} (Proved)