Question

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

Given: In a circle with centre B 

arc APC ≅ arc DQE

To Prove: Chord AC ≅ chord DE

Proof: In ΔABC and ΔDBE,

side AB ≅ side DB    ......`square`

side BC ≅ side `square`    .....`square`

∠ABC ≅ ∠DBE    ......[Measure of congruent arcs]

∆ABC ≅ ∆DBE    ......`square`

Answer 1

In ΔABC and ΔDBE,

side AB ≅ side DB    ......[Radii of the same circle]

side BC ≅ side BE    .....[Radii of the same circle]

∠ABC ≅ ∠DBE    ......[Measure of congruent arcs]

∴ ∆ABC ≅ ∆DBE    ......[SAS test of congruency]

∴ chord AC ≅ chord DE    ......[Corresponding sides of congruent triangles]