Segments AE and BD intersect at point C, and AB is parallel to DE. If AC = 12, CE = 8, and BD = 25, what is the length of BC?

Segments AE and BD intersect at point C, and AB is parallel... | SAT Lines, angles, and triangles Question, Answer Explained

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryHard

Segments $\overline{AE}$ and $\overline{BD}$ intersect at point $C$ , and $\overline{AB}$ is parallel to $\overline{DE}$ . If $AC = 12$ , $CE = 8$ , and $BD = 25$ , what is the length of $\overline{BC}$ ?

Student-produced response: enter your answer.

Show answer and explanation

Answer: 15

Because $\overline{AB}$ is parallel to $\overline{DE}$ , angles $BAC$ and $DEC$ are congruent alternate interior angles, and the vertical angles at $C$ are congruent. So triangle $ABC$ is similar to triangle $EDC$ , and $\frac{BC}{DC} = \frac{AC}{EC} = \frac{12}{8} = \frac{3}{2}$ . Since $BC + DC = BD = 25$ , $BC$ is $\frac{3}{5}$ of $25$ , which is $15$ .

Setting up $\frac{BC}{25} = \frac{12}{8}$ treats $\overline{BD}$ as if it were $\overline{DC}$ and gives $37.5$ , which is longer than $\overline{BD}$ itself.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free, or take a free full-length practice test.