3
In quadrilateral ABCD, the diagonals intersect each other at E such that
EA: EC = 3:2. Is ABCD a parallelogram? Give reasons for your answer
Answers
Answered by
14
Step-by-step explanation:
Here, ABCD is a quadrilateral with diagonals AC and BD intersect at point E.
⇒
EC
AE
=
ED
BE
[ Given ]
⇒
BE
AE
=
ED
EC
---- ( 1 )
In △ABE and △CDE,
⇒
BE
AE
=
ED
EC
] From ( 1 ) ]
⇒ ∠ABE=∠DEC [ Vertically opposites angles ]
∴ △ABE∼△CDE [ By SAS similarity theorem ]
⇒ ∠EDC=∠EBA [ Corresponding angles are equal. ]
∴ ∠BDC=∠ABD
Bu, this is a pair of alternate angles.
∴ AB∥DC
Thus, the quadrilateral ABCD is trapezium
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