Question

(1) The diagonals of cyclic quadrilateral ABCD are congruent. Show that AD = BC and seg AB || seg CD.​

Answer 1

Answer:

Step-by-step explanation:

Given : ABCD is a cyclic quadrilateral with AB║ CD

To prove AD =BC

Construction : Draw DE  ║AB

Proof : AB║CD

AD ║  BE By construction

Quadrilateral ADEB is a prallelogram

AB = DE  ..(1)  ( opposite sides are equal )

∠  BAD =∠ BED ...(2)  ( opposite angles are equal )

ABCD is a cyclic quadrilateral

∠BAD + ∠BCD  = 180 °...(3)  ( opposite angle of quadrilateral are supplementary)

∠BED  +∠ CED = 180° ..  ( linear pair )

∠BAD + ∠CED = 180° ..(4)

From (2) . (3) and (4)

∠BCD = ∠CED

∠ECD =∠ CED

DE = DC ( sides opposite to equal angles)

AD= BC ( From (1) )

Hence proved

Answer 2

Answer:

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