Question

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​

Answer 1

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