Constructing Perpendiculars to a Line

1. Constructing Perpendiculars to a Line Chapter 3 Lesson 3

2. Community Norms • We are all learners today • We are respectful of each other • We welcome questions • We welcome answers • We share discussion time • We turn off all electronic devices

3. Day / Date: Day 17 / September 12, 2013 • Topic: Constructing Perpendiculars to a Line • Activity:Using tools of Geometry construct and define Perpendiculars to a line • Textbook: Chapter 3, Lesson 3 • Pages: 154 - 156 • HomeLearning: Problems 1 - 10

4. Perpendiculars to a Line • Draw a line on your paper and label point P not on the line ● P

5. ● P • How you would construct the arcs on the line from point P? ● B ● A Swing equal arcs from point P that intersect the line at A and B.

6. ● P • How you would construct the arcs on the line from point P? ● B ● A How is PA related to PB? Hint: review the Converse of the Perpendicular Bisector Conjecture

7. ● P • Now construct the arcs below the line. ● B Now use the straightedge to connect P to the line but stop at the line. ● A

8. ● P • Label the midpoint M ● B ● A M

9. You now have constructed a perpendicular through a point not on the line. • Now randomly place 3 points on line AB and label them as Q, R, and S. • Connect P to point Q, R and S.

10. Which line is the shortest? • Now, state your observations by completing the following conjecture.

11. Shortest Distance Conjecture (C-7) • The shortest distance from a point to a line is measured along the from the point to the line. perpendicular segment

12. Definition: Distance from a Point to a Line • The distance from a point to a line is the length of the perpendicular segment from the point to the line.

13. Altitude of a Triangle • An altitude of a triangle is a perpendicular segment from a vertex to the opposite side or to a line containing the opposite side.

14. An altitude can be made inside the triangle.

15. An altitude can be outside the triangle.

16. An altitude can be one of the sides of the triangle.