Question in-the

4.1 Lines, Angles, and Triangles - Angle relationships (parallel lines)
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The figure presents quadrilateral A, C D F, where side A, F and side C D are horizontal, and side C D lies above side A, F. Side C D is longer than side A, F. Point B lies on left side A, C, and point E lies on right side D F. Line segment B E, which is horizontal, divides quadrilateral A, C D F into two quadrilaterals, A, B E F and B C D E.

In the figure above, side A, F , line segment B E , and side C D are parallel. Points B and E lie on side A, C  and side F D , respectively. If the length of line segment A, B equals 9, the length of line segment B C equals 18 point 5, and the length of line segment F E equals 8 point 5, what is the length of line segment E D , to the nearest tenth?

A.

16.8

B.

17.5

C.

18.4

D.

19.6

In the figure above, , , and are parallel. Points B and E lie on and

Medium-difficulty · SAT Math · Lines, Angles, and Triangles — Angle relationships (parallel lines). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice B is correct. Since line segment A F, line segment B E, and line segment C D are parallel, quadrilaterals A F E B and B E D C are similar. Let x represent the length of line segment E D. With similar figures, the ratios of the lengths of corresponding sides are equal. It follows that 9 over 18 point 5, equals 8 point 5 over x. Multiplying both sides of this equation by 18.5 and by x yields 9 x equals, 18 point 5, times 8 point 5, or 9 x equals 157 point 2 5. Dividing both sides of this equation by 9 yields x equals 17 point 4 7, which to the nearest tenth is 17.5.

Choices A, C, and D are incorrect and may result from errors made when setting up the proportion.