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

1Serra - Discovering GeometryChapter 3: Using Tools of Geometry

Sketch, Draw, ConstructWhen 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.

draw

sketch

construct

Serra - Discovering GeometryChapter 3: Using Tools of Geometry

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

Building/Dropping A Perpendicular

Building/Dropping A Perpendicular

Altitudes

A

C

B

Circumcenter.

Altitudes

A

C

B

Orthocenter.

8

1. Draw a line m and a point P on the line.2. Put the point of the compass on P.

Stretch out the compass as far as you like.

3. Draw an arc on the left and right so that they intersect the line.

4. Put the point of the compass on the intersection (X) on the left. Stretch out the compass til it’s past P.

5. Draw an arc above or below point P.6. Without changing the compass, put the

point on the X on the right and draw another arc. You should now have an X.

7. Connect P and the X with a line. Show that the lines are perpendicular.

Serra - Discovering GeometryChapter 3: Using Tools of Geometry

Construction 4: Perpendicular to a Line from a Point ON the Line

P

1 2

3 4

5

http://www.mathopenref.com/constperplinepoint.html

9

1. Draw a line m and a point P not on the line.

2. Put the point of the compass on P. Stretch out the compass until it passes the line.

3. Draw an arc on the left and right so that they intersect the line.

4. 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.

5. Draw an arc on the side opposite point P.

6. 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.

7. Connect P and the X with a line. Show that the lines are perpendicular.

Serra - Discovering GeometryChapter 3: Using Tools of Geometry

Construction 5: Perpendicular to a Line from a Point OUTSIDE the Line

P

1 2

3 4

5

http://www.mathopenref.com/constperpextpoint.html

• Draw a large obtuse triangle on a half sheet of paper.

• Construct the altitude from each vertex.