SOLUTION: A line, which goes through the point of intersection of the diagonals of a trapezoid, divides one of the bases into two segments. The ratio of the length of these segments is m:n.

Algebra ->  Polygons -> SOLUTION: A line, which goes through the point of intersection of the diagonals of a trapezoid, divides one of the bases into two segments. The ratio of the length of these segments is m:n.       Log On


   

Question 1134336: A line, which goes through the point of intersection of the diagonals of a trapezoid, divides one of the bases into two segments. The ratio of the length of these segments is m:n. What is the ratio of the length of the segments of the other base?
Answer by greenestamps(13200) About Me  (Show Source):
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When the diagonals of a trapezoid are drawn, the two triangles formed by the diagonals and the two bases of the trapezoid are similar.

Any line through the point of intersection of the two diagonals will then divide those two similar triangles into two pairs of similar triangles. So the ratio into which the line divides one of the bases is the same as the ratio in which it divides the other base.

ANSWER: The ratio of the lengths of the segments of the other base is also m:n.