Question

if AC = 2, CD = 6, and CE = 3, what is BC? .. 12, 11 , 9 or 4

Answer 1

is their any diagram given

Answer 2

Yes

Answer 3

so attach the diagram

Answer 4

/Users/eileenquinones/Desktop/Screen Shot 2014-12-10 at 5.12.48 PM.png

Answer 5

in \(\triangle ACB \) and \(\triangle ECD\)

1.) \(\angle ACB\cong \angle ECD\)-----(vertical angle)
as lines AB and DE are parallel

hence

2.) \(\angle ABC\cong \angle EDC\)------------(alternate interior angle)

3.) \(\angle BAC\cong \angle CED\)------------(alternate interior angle)

so \(\triangle ACB \) \(\approx\) \(\triangle ECD\)
by \(AAA \) similarity theorm

hence
\(\dfrac{AC}{BC}=\dfrac{CE}{CD}\)


\(\dfrac{2}{BC}=\dfrac{3}{6}\)


\(BC=\dfrac{2\times 6}{3}\\
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\huge
BC=4\)

Answer 6

thank you!