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

Proof:

In ΔABC and ΔDBE,

side AB ≅ side DB   ...\[\boxed{\text{[Radii of the same circle]}}\]

side BC ≅ side \[\boxed{\text{BE}}\]   ...\[\boxed{\text{[Radii of the same circle]}}\]

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

∴ ∆ABC ≅ ∆DBE   ...\[\boxed{\text{[SAS test of congruency]}}\]

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