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Prove and apply theorems about perpendicular lines.

Objective. Prove and apply theorems about perpendicular lines. Vocabulary. perpendicular bisector distance from a point to a line. _______________________ – a line perpendicular to a segment at the segment’s midpoint.

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Prove and apply theorems about perpendicular lines.

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  1. Objective Prove and apply theorems about perpendicular lines.

  2. Vocabulary perpendicular bisector distance from a point to a line

  3. _______________________– a line perpendicular to a segment at the segment’s midpoint. _______________________– the length of the perpendicular segment from the point to the line (which is the shortest segment from a point to a line.)

  4. A. Name the shortest segment from point A to BC. Example 1: Distance From a Point to a Line B. Write and solve an inequality for x.

  5. C. Name the shortest segment from point A to BC. Ex.1 D. Write and solve an inequality for x.

  6. HYPOTHESIS CONCLUSION

  7. Example 2A: Proving Properties of Lines Write a two-column proof. Given: r || s, 1  2 Prove: r  t

  8. Given: Prove: Example 2B Write a two-column proof.

  9. Example 3A: Carpentry Application A carpenter’s square forms a right angle. A carpenter places the square so that one side is parallel to an edge of a board, and then draws a line along the other side of the square. Then he slides the square to the right and draws a second line. Why must the two lines be parallel?

  10. Example 3B A swimmer who gets caught in a rip current should swim in a direction perpendicular to the current. Why should the path of the swimmer be parallel to the shoreline?

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