Question

1) In the given figure ABCD is
cyclic quadrilateral in which
angle ABC = BCD
To prove :
side DC congruent side AB and ADIlBC.
​

Answer 1

Step-by-step explanation:

Given:ABCD is a cyclic quadrilateral Ab ll CD

To prove DC ll AB

AD ll BE by construction

Quadrilateral is a parallelogram

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

then, angle BED=BAD (2) (opposites angle are =)

ABCD a cyclic quadrilateral

angle BAD + BED= 180 degree (opposite angle of an quadrilateral are supplementary)

Angle BED+CED = 180 degree (by linear pair)

Angle BAD+CED= 180 degree (4)

From 2,3 and 4

Angle BCD = CED

Angle ECD = CED

DE = DC by (1)

AD = BC by (1)

Hence proved!