Question

Please help.. 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.


Answer choices:
Segment BD = 12

Segment BD = 4

Segment BF = 16

Segment BF = 9

Answer 1

First, find the length of EF via the Pythagorean theorem: 24^2+18^2=c^2. Once you find the value of EF, you also know the value of BD because it's parellel and you can consider options A and B.
For options C and D, you know have the value of BD. Treat the whole figure as a triangle and solve for the length of the base, again with the Pythagorean theorem:
c^2=a^2+b^2
c^2 = (12+18)^2 + (6 + x)^2
where x is the length of BD.

Answer 2

parallel*
After you find the length of the entire base, you can subtract 24 to find the length of BF and consider choices C and D.