Mathematics: 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: which statement can be proved true using the given theorem? segment bf = 16 segment bd = 20 segment bd = 15 segment bf = 32

Around 4-5 :) hope this helps...

Theorem: a line parallel to one side of a triangle

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19.06.2020

Segment BF = 16 is true.

Step-by-step explanation:

Since, DE is parallel to BC, so DE will divide AB and AC proportionally.

Hence,

$\frac{AE}{EC} = \frac{AD}{DB}$

⇒ $\frac{12}{18} = \frac{6}{DB}$

{Since, given that AE = 12, EC = 18 and AD = 6}

⇒ BD = 9.

Again, since, EF is parallel to AB, so EF will divide BC and AC proportionally.

Hence, $\frac{CE}{AE} = \frac{FC}{BF}$

⇒ $\frac{18}{12} = \frac{24}{BF}$

{Since, given that AE = 12, EC = 18 and FC= 24}

⇒ BF = 16.

Therefore, segment BF = 16 is true. (Answer)

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