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Question

# In a quadrilateral ABCD,which is not a trapezium,it is know that ∠DAB=∠ABC=60. Moreover,∠CAB=∠CBD. Then:

A
AB=BC+CD
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B
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C
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D
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Solution

## The correct option is C AB=BC+ADIn quadrilateral ABCD,∠DAB=∠ABC=60o [ Given ] ∠CAB=∠CBD [ Given ]⇒ BC and AD are produced to intersect at E.In △ABE,∠EBA=∠EAB=60o∴ ∠BEA=60o [ Since, sum of angles of triangle is 180o ]∴ △ABE is an equilateral triangle.⇒ AB=BE=EA ---- ( 1 )In △ABC and △BED⇒ ∠BED=∠CBA=60o⇒ ∠EBD=∠CAB [ Given ]⇒ BE=AB [ From ( 1 ) ]∴ △ABC≅△BED [ By ASA congruence rule ]⇒ DE=BC [ Corresponding sides of congruent triangles ] --- ( 2 )⇒ AB=AE⇒ AB=AD+DE ⇒ AB=AD+BC [ From ( 2 ) ]

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