Question

How do I solve this?

Answer 1

See below.

Explanation:

Use the converse of the Triangle Proportionality Theorem.

If a segment divides two sides of a triangle into proportional lengths, then the segment is parallel to the third side of the triangle.

Here we have triangle CED.

Segment AB divides sides EC and ED.

Side EC is divided into segments EA and AC.

Side ED is divided into segments EB and BD.

Now we check the ratios of the lengths of the segments.

Is EA/AC = EB/BD?

EA/AC = 3.75/5 = 0.75

EB/BD = 4.5/6 = 0.75

Since the ratios are equal, the segment, AB, is parallel to the third side of the triangle, CD.

Answer 2

AB and CD are parallel because when 2 lines in a plane are parallel it means they do not intersect