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McGraw Hill Integrated II, 2012 View details

4. Parallel Lines and Proportional Parts

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Exercise 51 Page 580

Use the Triangle Proportionality Theorem to figure out how to draw the required segments.

See solution.

Practice makes perfect

Let's start by drawing PQ of length a.

Next, let's draw a second segment QR of length b such that P, Q, and R are collinear.

Now, we draw PS of length c, such that S is not collinear to the three previous points.

To draw the fourth segment we are looking for, first we draw PS and QS. Then, we draw a line parallel to QS passing through R.

The fourth required segment is ST whose length is d. Notice that the Triangle Proportionality Theorem gives us the required proportion. a/b = c/d ✓ Keep in mind that the segments drawn above are just an example and your diagram may vary.