Question

The chords corresponding to congruent arcs of a circle are congruent. Prove the theorem by completing following activity.​

Answer 1

Answer:

Given: B is the centre of circle. arc APC ≅ arc DQE To prove: chord AC ≅ chord DE Proof: [m(arc APC) = ∠ABC (i) [Definition of measure of m(arc DQE) = ∠DBE] (ii) minor arc] arc APC ≅ arc ∠DQE (iii) [Given] ∴ ∠ABC ≅ ∠DBE [From (i), (ii) and (iii)] In ∆ABC and ∆DBE, side AB ≅ side DB [Radil of the same circle] side [CB] side [EB] [Radii of the same circle] ∠ABC ≅∠DBE

∴ ∆ABC ≅ ∆DBE [SAS test of congruency] ∴ chord AC ≅ chord

Step-by-step explanation:

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