Line Segments Divided Proportionally

Line Segments Divided Proportionally

How to solve problems about the line segments which are divided proportionally: examples and their solutions.

Example 1

Find the value of x. The measures of the line segments divided by three parallel lines: 8, 16, x, and 18.

Three horizontal lines are parallel.
And they divide two transversals.

Then the transversals are divided proportionally:
8 / 16 = x / 18.

Example 2

Find the value of x. The measures of the line segments divided by three parallel lines: 6, 4, 11 - x, and x.

Three vertical lines are
all perpendicular to the bottom line.

Then, by the perpendicular transversal theorem,
three vertical lines are all parallel to each other.

And the vertical lines divide two transversals.
(upper line, bottom line)

So the transversals are divided proportionally:
11 / x = (6 + 4) / 4.