Question

Which of the following theorems states, “If a line divides two sides of a triangle proportionally, it is parallel to the third side.”? Triangle Proportionality Theorem Converse of the Triangle Proportionality Theorem Pythagorean Theorem Converse of the Pythagorean Theorem.

Answer 1

The answer is Converse of the Pythagorean theorem

Explanation:

Answer 2

Converse of triangle proportionality theorem

Explanation:

We are given that in a triangle ABC, D and E are some points in AB and AC respectively.

D and E divide AB and AC such that

AD/DB =AE/DC

To prove that DE is parallel to third side BC>

This can be proved using converse of triangle proportionality theorem

REcollect the triangle proportionality theorem that

If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion

So converse is is a line intersects the other sides make proportional intercepts then the line is parallel to the third side.