1.

6 Prove that is a line divides any two sides of a triangle in the same ratio then the line is parallel to the third side​

Answer»

Answer:

According to this theorem, if a line divides any two sides of a triangle in the same ratio, then the line is PARALLEL to the THIRD side. Assume DE is not parallel to BC. Now, draw a line DE' parallel to BC. This is possible only when E and E' coincides.

Step-by-step explanation:

Suppose a line DE, intersects the two sides of a triangle AB and AC at D and E, such that;

AD/DB = AE/EC ……(1)

Assume DE is not parallel to BC. Now, draw a line DE’ parallel to BC.

Hence, by similar triangles,

AD/DB = AE’/E’C ……(2)

From eq. 1 and 2, we get;

AE/EC = AE’/E’C

Adding 1 on both the sides;

AE/EC + 1 = AE’/E’C +1

(AE +EC)/EC = (AE’+E’C)/E’C

AC/EC = AC/E’C

So, EC = E’C

This is possible only when E and E’ coincides.

But, DE’//BC

Therefore, DE//BC.

Hence, PROVED.


Discussion

No Comment Found

Related InterviewSolutions