3.3 Constructing Perpendicular to a Line

1. 3.3 Constructing Perpendicular to a Line Objectives: I CAN discover methods of constructing a perpendicular to a line from a point not on the line and from a point on the line. I CAN determine a method of find the shortest path from a point to a line Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

2. Sketch, Draw, Construct draw When you ___________ an equilateral triangle, you should use you geometry tools for accuracy. You may use a protractor to measure angles and a ruler to measure the sides. When you ___________ an equilateral triangle, you freehand a triangle that looks like an equilateral triangle. No geometry tools needed. When you ___________ an equilateral triangle with a compass and straightedge, you don’t rely on measurements from a protractor or a ruler. This guarantees that you triangle is equilateral. sketch construct Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

3. Investigations 1 & 2: p.152-153 Finding the Right Line C7 Shortest Distance Conjecture The shortest distance from a point to a line in measured along the ________________ from the point to the line. perpendicular segment

4. Building/Dropping A Perpendicular

5. Building/Dropping A Perpendicular

6. Altitudes Circumcenter. A C B

7. Altitudes Orthocenter. A C B

8. Construction 4: Perpendicular to a Line from a Point ON the Line • Draw a line m and a point P on the line. • Put the point of the compass on P. Stretch out the compass as far as you like. • Draw an arc on the left and right so that they intersect the line. • Put the point of the compass on the intersection (X) on the left. Stretch out the compass til it’s past P. • Draw an arc above or below point P. • Without changing the compass, put the point on the X on the right and draw another arc. You should now have an X. • Connect P and the X with a line. Show that the lines are perpendicular. 5 P 1 2 3 4 http://www.mathopenref.com/constperplinepoint.html Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

9. Construction 5: Perpendicular to a Line from a Point OUTSIDE the Line • Draw a line m and a point P not on the line. • Put the point of the compass on P. Stretch out the compass until it passes the line. • Draw an arc on the left and right so that they intersect the line. • Put the point of the compass on the intersection (X) on the left. Stretch out the compass til it’s more than half the distance between the X’s. • Draw an arc on the side opposite point P. • Without changing the compass, put the point on the X on the right and draw an arc on the side opposite point P. You should now have an X. • Connect P and the X with a line. Show that the lines are perpendicular. 5 P 1 2 3 4 http://www.mathopenref.com/constperpextpoint.html Serra - Discovering Geometry Chapter 3: Using Tools of Geometry

10. Draw a large obtuse triangle on a half sheet of paper. • Construct the altitude from each vertex.