ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE)= ar(BCF)
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It is given that ABCD is a parallelogram. We know that opposite sides of a parallelogram are equal.
∴ AD = BC ... (1)
Similarly, for parallelograms DCEF and ABFE, it can be proved that
DE = CF ... (2)
And, EA = FB ... (3)
In ΔADE and ΔBCF,
AD = BC [Using equation (1)]
DE = CF [Using equation (2)]
EA = FB [Using equation (3)]
∴ ΔADE ≅ BCF (SSS congruence rule)
⇒ Area (ΔADE) = Area (ΔBCF)
∴ AD = BC ... (1)
Similarly, for parallelograms DCEF and ABFE, it can be proved that
DE = CF ... (2)
And, EA = FB ... (3)
In ΔADE and ΔBCF,
AD = BC [Using equation (1)]
DE = CF [Using equation (2)]
EA = FB [Using equation (3)]
∴ ΔADE ≅ BCF (SSS congruence rule)
⇒ Area (ΔADE) = Area (ΔBCF)
Answered by
0
Answer:
They are Equal!
Step-by-step explanation:
Since ABCD is a parallelogram, therefore sides AD and BC are equal.
Since DCFE is also a parallelogram, therefore, sides DE and FC are equal.
Since ABFE is also a parallelogram, therefore, sides AE and BF are equal.
So, triangles ADE and BCF are congruent by SSS congruency rule.
∴ Corresponding angles are equal in both triangles .
So, the areas will be equal.
Therefore ar(ADE)=ar(BCF).
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