Suppose in a quadrilateral ABCD, AC = BD and AD = BC. Prove that ABCD is a trapezium.
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Given :
ABCD is a Quadrilateral .
AC = BD , AD = BC
To prove : ABCD is a trapezium .
Proof : In ∆ABD and ∆ABC
AC= BD ( given )
AD = BC ( given )
BC = BC ( common side )
Therefore ,
∆ABD is congruent to ∆ABC
Area of ∆ABD = Area of ∆ABC
AB // CD
[ By theorem ,
Two triangles having the same base
and equal areas will lie between the
same parallels .
Therefore ,
In ABCD Quadrilateral AB//CD
it is a Trapezium.
•••••
ABCD is a Quadrilateral .
AC = BD , AD = BC
To prove : ABCD is a trapezium .
Proof : In ∆ABD and ∆ABC
AC= BD ( given )
AD = BC ( given )
BC = BC ( common side )
Therefore ,
∆ABD is congruent to ∆ABC
Area of ∆ABD = Area of ∆ABC
AB // CD
[ By theorem ,
Two triangles having the same base
and equal areas will lie between the
same parallels .
Therefore ,
In ABCD Quadrilateral AB//CD
it is a Trapezium.
•••••
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