1. Parallel Lines and Proportions Slideshow 36, Mathematics Mr. Richard Sasaki, Room 307

2. ObjectivesObjectives Understand ratios of lengths intercepted by parallel lines (the intercept theorem) Understand ratios of lengths intercepted by parallel lines (the intercept theorem) Be able to find missing line segments of lines Be able to find missing line segments of lines Separate line segments into given ratios Separate line segments into given ratios

3. Parallel Lines Parallel lines are equal distances apart at all lengths and. infinite in length Look at the diagram below. D E F G We can say. Note: Vertices should be labelled on lines. Let’s add some more lines. No, because they aren’t necessarily parallel. But if we had another line, could there be some relationship?

4. The Intercept Theorem A A’ B B’ C C’ X Something that is generally known once proved.

5. Answers - Easy Answers - Hard The other way around is fine!

6. The Intercept Theorem (Reverse) If we have line segment lengths where pairs are in the same proportion, we can show that lines (or line segments) are parallel. Example A line that passes through a triangle is parallel to its base if both are similar. If they are parallel, what must be true?

7. Ratios and Line Segments With the use of a ruler, we can divide line segments into smaller proportions. Example (Lying on one line). 5

8. AnswersAnswers