Question

Theorem: The chords corresponding to congruent arcs of circle are congruent.
Given : In a circle with centre B arc APC congruent to arc DQE
To Prove: Chord AC chord DE
Proof: (Fill in the blanks and complete the
proof)
In triangle ABC and DBE.
side AB side DB (....)
side .... side ................)
ABC congruent to ZDBE measures of congruent
arcs
.: triangle ABC congruent to DBE
chord AC chord DE (.....)​

Answer 1

Answer:

[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 [From (iii), Measures of congruent arcs] ∴ ∆ABC ≅ ∆DBE [SAS test of congruency] ∴ chord AC ≅ chord DE [c.s.c.t]

Answer 2

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 [From (iii), Measures of congruent arcs] ∴ ∆ABC ≅ ∆DBE [SAS test of congruency] ∴ chord AC ≅ chord DE [c.s.c.t]Read more on Sarthaks.com - https://www.sarthaks.com/851450/theorem-chords-corresponding-congruent-circle-congruent-circles-congruent-centre-circle

Step-by-step explanation:

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