Parallelogram abcd is given. draw line ef so that it goes through the vertex a. point e lies on the side bc and point f lies on the extension of dc . prove that △abe∼△fce.

Given: ABCD is a parallelogram,

In which E ∈ BC and F lies on the extension of DC,

Such that line segment EF goes through the vertex A.

To prove:

Proof:

Since, By the definition of parallelogram,

By the Alternative interior angle theorem,

Also, ( vertically opposite angles )

Thus, By AA similarity postulate,

Hence proved.

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