Question

A point e is taken on the side bc of a parallelogram abcd. Ae and dc are produced to meet at f. Prove thatar adf=area of abfc

Answer 1

Answer:

Step-by-step explanation:

Given: ABCD is a parallelogram.

A point E is taken on the side BC.

AE and DC are produced to meet at F.

To prove: ar(∆ADF)=ar(∆ADF)......(1)

Proof:

As DC||AB,

So CF||AB

Since triangles on the same base and between the same parallels are equal in area,so we have ar(∆ACF)=ar(∆BCF).....(2)

Adding(1) and (2),we get

ar(∆ADC)+ar(∆ACF)=ar(∆ABC)+ar(∆BCF)

=ar(∆ADF)=ar(ABFC).

Hence, proved.

Answer 2

Answer:

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