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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`
Solution
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]
RELATED QUESTIONS
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