How do you do Test 2 Section 3 Number 18?

The key here is to recognize that you’re dealing with similar triangles (pro tip: similar triangle questions often take this “hourglass” form). The two angles at point B are vertical, so they must be congruent. And because segments AE and CD are parallel, you’ve got alternate interior angles for the rest. When all the angles in two triangles are congruent, those triangles are similar.

(It might be easier to see the alternate interior angles if you extend the lines…expand the image on the right.)

Anyway, now that you’ve established that these are similar triangles, you just need to use ratios to solve. If AB=10 and [latexBD=5[/latex], then each set of corresponding sides will be in the same ratio. So we can solve for BC thusly:

    \begin{align*}\dfrac{AB}{BD}&=\dfrac{BE}{BC}\\\\\dfrac{10}{5}&=\dfrac{8}{BC}\\\\2&=\dfrac{8}{BC}\\BC&=4\end{align*}

But wait—you’re not quite done! The question asks for CE, not BC!

CEBCBE = 4 + 8 = 12

There. Now you’re done.