Question

prove that the chord corresponding to congruent arcs of a circle are congruent​

Answer 1

Answer:

Given: In congruent circles with centres B and R,

 arc APC ≅ arc DQE

To prove: chord AC ≅ chord DE

Proof:  [m(arc APC) = ∠ABC (i)

m(arc DQE) = ∠DRE] (ii)

[Definition of measure of minor arc]  

arc APC ≅ arc DQE (iii) [Given]

∴ ∠ABC = ∠DRE (iv) [From (i), (ii) and (iii)]

In ∆ABC and ∆DRE,  

[side AB ≅ side DR [Radii of congruent circles]

 side CB ≅ side ER] [From (iv)]

∠ABC ≅ ∠DRE

∴ ∆ABC ≅ ∆DRE [SAS test of congruency]