Question

If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third line..



❣proof that❣

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Answer 1

If a line divides any two sides of the triangle in the same ratio, then the line is parallel to the third side. So we have to prove DE | | BC .To prove DE | | BC let us assume as DE is not parallel to BC. That method is called contradiction method from that method , we can easily prove the desired statement. So for using contradiction method, we have to assume at starting the opposite of the required proof,

And that is not necessary , As you can proof that by different method As , well ,

As :

Diagram In Above Pic

In ∆ ABC

BDDA = CEEA ( Given )

1 + BDDA = CEEA + 1

DADA + BDDA = CEEA + EAEA

DA + BDDA = CE + EAEA

ABAD = ACAE

Hence

∆ ABC similar to ∆ ADE

So

∠ ADE = ∠ ABC (corresponding angles of similar triangles are equal)

So,

BC | | DE ( Hence proved )

Hope this information will clear your doubts about topic.