Question

Theorem: a line parallel to one side of a triangle divides the other two proportionately. In the figure shown below, segment DE is parallel to segment BC and segment EF is parallel to AB. Which statement can be proved true using the given theorem?

Answer 1

Answer:

the answer is B because to parallel segs always match with

seg=18

Step-by-step explanation:

Answer 2

Answer:

BD = 20

BF = 18

Step-by-step explanation:

According to the given theorem, we can elaborate the following proportions

$\frac{AD}{DB}=\frac{AE}{EC}$ and $\frac{CE}{EA}=\frac{CF}{FB}$

Using these proportions we can find sides DB and FB.

Replacing all values, we have

$\frac{AD}{DB}=\frac{AE}{EC}\\\frac{12}{BD}=\frac{15}{25}\\ BD=\frac{300}{15}\\ BD=20$

$\frac{CE}{EA}=\frac{CF}{FB}\\\frac{25}{15}=\frac{30}{BF}\\BF=\frac{450}{25}\\ BF=18$

Therefore, the right asnwers are BD = 20 and BF = 18