Question

Theorem: A line parallel to one side of a triangle divides the other two proportionately.

In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

The figure shows triangle ABC with segments DE and EF. Point D is on side AB, point E is on side AC, and point F is on side BC. Segment AD is 6, segment AE is 12, segment EC is 18, and segment FC is 24.

Which statement can be proved true using the given theorem?

Segment BD = 12
Segment BD = 4
Segment BF = 16
Segment BF = 9

Answer 1

Answer:

Segment BF = 16

Step-by-step explanation:

Side EC corresponds to side AC. AC is made of AE and EC.

AE = 12, EC = 18. so side AC = 30.

We can think of side AC as the side in the big triangle and side EC of being in the meduim triangle.

The next step is to find the proportion of EC and AC so 18/30 = 0.6. This is the proportion between the medium triangle and the big triangle.

Side BC is made up of BF and FC. BF is unknown and FC = 24. Side BC is a side in the big triangle and FC is a side in the medium triangle. Since we know the proportion already, to find the length of BC we do 24/0.6 = 40.

40 = BC

40 = FC + BF

40 = 24 + BF

16 = BF