Question

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

Here, ABCD is a quadrilateral with diagonals AC and BD intersect at point  E.

⇒  ECAE=EDBE               [ Given ]

⇒  BEAE=EDEC         ---- ( 1 )

In △ABE and △CDE,

⇒  BEAE=EDEC              ] 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.

Answer 2

Answer:

AB||DC

Step-by-step explanation:

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