Lines, Angles, and Triangles

SAT Math· difficulty 4/5

In the figure, lines ell1parallelell2parallelell3\\ell_1 \\parallel \\ell_2 \\parallel \\ell_3. A transversal crosses all three lines. The segment between ell1\\ell_1 and ell2\\ell_2 has length 3 and the segment between ell2\\ell_2 and ell3\\ell_3 has length 4. Another transversal cuts the parallel lines such that its segment between ell1\\ell_1 and ell2\\ell_2 has length 6. What is the length of its segment between ell2\\ell_2 and ell3\\ell_3?

  • A

    12

  • B

    246\frac{24}{6}

  • C

    64\frac{6}{4}

  • D

    8

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Explanation

Parallel lines cut transversals in proportional segments: frac34=frac6x\\frac{3}{4} = \\frac{6}{x}, so 3x=243x = 24, x=8x = 8.

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