explain converse of cyclic quadrilateral with proff
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Answer:
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Step-by-step explanation:
Given: In ABCD, ∠A + ∠C = 180°
To Prove: ABCD Is A Cyclic Quadrilateral
Construction: Draw A Circle Through Three Non-Collinear Points A, B And
D. Suppose Point C Does Not Lie On The Circle. Extend DC
If Required To Intersect The Circle At E. Join BE.
Proof: Indirect Proof
ABED Is A Cyclic Quadrilateral __________(Construction)
∴ ∠A + ∠E = 180° _____(1)____(Theorem On Cyclic Quadrilateral)
∴ ∠A + ∠C = 180° ______(2)_____(Given)
∴ ∠A + ∠E = ∠A + ∠C __________[From (1) And (2)
∴ ∠E = ∠C
i.e ∠DEB = ∠BCE
But ∠DEB Is An Exterior ∠ Of ΔBCE
∴ ∠DEB ≠ ∠BCE
Hence, Points C And E Coincide
∴ The Circle Passing Through A, B And D Also Passes Through C
∴ ABcD Is A Cyclic Quadrilateral