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Constructing Perpendiculars to a Line. Chapter 3 Lesson 3. 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. Day / Date: Day 17 / September 12, 2013
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Constructing Perpendiculars to a Line Chapter 3 Lesson 3
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
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
Perpendiculars to a Line • Draw a line on your paper and label point P not on the line ● P
● 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.
● 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
● 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
● P • Label the midpoint M ● B ● A M
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.
Which line is the shortest? • Now, state your observations by completing the following conjecture.
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
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.
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.