Question

In the given figure, ABED is a parallelogram in which DE = EC. Show that

ar (ABF) = ar (BEC).​

Answer 1

Step-by-step explanation:

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Answer 2

It is shown that area(ΔABF)=area(ΔBEC)

Step-by-step explanation:

Given, ABCD is a parallelogram where DE=EC

To prove,

area(ΔABF)=area(ΔBEC)

Sol.

It is given that ,

AB=DE ( Opposite sides of a parallelogram are always equal)

Also, DE=EC (Given)

∴ AB=EC, Also AB ║ DE

Since Opposite side of parallelogram are always parallel  

⇒AB ║ DC

Now, ΔABF and ΔBEC  have equal base AB and EC and between the same parallel line AB and DC.

Therefore,area(ΔABF) = area(ΔBEC)

Hence Proved