Question

HELP! <3 I have other questions as well not yet posted, if you'd like more points! :3

Answer 1

Option B: $\frac{AB}{BC}=\frac{AE}{ED}$ is sufficient to prove that $BE$ ll $CD$

Explanation:

Given that ACD is a triangle.

The line EB intersects the sides AC and AD of the triangle.

The point E intersect the side AD and B intersect the side AC.

We need to prove that $BE$ ll $CD$

Then, the side splitter theorem states that "If a line intersects two sides of a triangle and divides the sides proportionally, the line is parallel to the third side of the triangle".

From the side splitter theorem, the line EB intersects the two sides of the triangle AC and AD and divides the sides proportionally.

Thus, the proportion of the sides is given by

$\frac{AB}{BC}=\frac{AE}{ED}$

This proportionality shows that the line is parallel to the third side of the triangle.

Hence, $\frac{AB}{BC}=\frac{AE}{ED}$ is sufficient to prove that $BE$ ll $CD$

Therefore, Option B is the correct answer.