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Question

ABCD is quadrilateral in which ABCD. If AD=BC, show that A=B and C=D

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Solution


Here, ABCD [Given]

and ADEC [By construction]

AECD is a parallelogram.

AD = EC [Opposite sides of parallelogram are equal]

But AD = EC [Given]

EC = BC

CBE = CEB ---- ( 1 )

B + CBE = 180 [Linear pair] ---- ( 2 )

ADEC [By construction]

and transeversal AE intersects them

A + CEB = 180 ---- ( 3 )

[Sum of adjacent angles of parallelogram is supplementary ]
B + CEB = 180 [From ( 2 ) and ( 3 )]

But CBE = CEB [From ( 1 )]

A=B [Proved] -- ( 4 )

ABCD

A + D = 180 [Sum

Supplementary angles of parallelogram is 180]

and B + C = 180

A + D = B + C

But A = B [From ( 4 )]

C=D


825141_570415_ans_a2b65d550d75482c9ab24b49f6380527.png

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