Question

We can tell that side DE is parallel to side....

Answer 1

By the converse of the basic proportionality theorem, we can say DE║AB.

We need to check whether DE is parallel to AB.

What is the converse of the basic proportionality theorem?

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

In triangle ABC, we can see on side AC, D is midpoint (∵AD=DC) and on side BC, E is midpoint (∵BE=CE).

Therefore, by the converse of the basic proportionality theorem, we can say DE║AB.

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Answer 2

The proof is shown below:

What is Mid point theorem?

The line segment joining the mid points of any two sides of a triangle is parallel to the third side.

△ABC in which D and E are the mid points of AB and AC,.

If D and E are the mid points of AB and AC,

then AD=DB and AE=EC.

Thus,

AD/DB = AE/ EC

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by the converse of Thales theorem, DE∥BC.

As, by theorem we can say that DE∥BC.

So, there is no other side parallel to DE.

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