In square ABCD, diogonals AC and BD intersect each other at point E. If AE/EC=BE/ED then complete the following activity to prove square is a trapezium
Answers
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.
Answer:
hope it help
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.