1. Duplicating (copying) a segment2. Duplicating (copying) an angle3. Constructing the bisector of a segment (bisecting a segment)4. Constructing an angle bisector (bisecting an angle)5. Constructing a perpendicular bisector of a line segment6. Constructing a perpendicular from a point not on a line to the line(perpendicular lines)7. Constructing a line parallel to a given line through a point not onthe line

Topic 1Chapter 3: ConstructionsGreek philosopher PlatoEuclid(Elements)

1.(3.2)Constructing Perpendicular bisectors2.(3.3)Constructing perpendiculars to a line

(perpendicular from a point not on a line to the line)

3.(3.4) Constructing an angle bisectors (bisecting an angle)

4.(3.5) Constructing parallel linesthe line

3.2: Constructing the perpendicular bisector of a segment

Segment bisector: Is a line, ray, or segment that passes through the midpoint of a segment .

Perpendicular bisector: It is a bisector that is also perpendicular to the segment.

Textbook, page 149Patty Paper InvestigationInvestigation 1: Finding the right bisector

Textbook, page 150Investigation 2: Constructing thePerpendicular bisector

You Tube: Constructing the perpendicular bisector

https://www.youtube.com/watch?v=XXI60B3m70Y

If Line AC is the Perpendicular bisector of Segment PQ, then BP=BQ

Perpendicular Bisector Theorem: If a point is on theperpendicular bisector of a segment, then it is

equidistant from the endpoints.

Converse of the Perpendicular Bisector Theorem: If a point is equidistant from the endpoints of a segment , then it is on the perpendicular bisector of the segment.

If BP=BQ, thenLine AC is the Perpendicular bisector of Segment PQ.

Homework:Workbook 3.2Exercise 1.Describe each step

3.3: Constructing Perpendiculars to a Line

Shortest Distance Theorem:The shortest distance from a point to a line is measuredalong the perpendicular segment from the point to the

line.

The distance from point Pto line AS is the length of segment PM.

Textbook, page 154Patty Paper InvestigationInvestigation 1: Finding the Right Line

Textbook, page 155Investigation 2: Patty-Paper Perpendiculars

You Tube: Constructing the perpendicular bisector

https://www.youtube.com/watch?v=I4dh2R6b1N0

Homework:Draw a line anda point not on the line.Construct the perpendicular from thatpoint to that line. Describe each step.

3.4: Constructing Angle Bisectors

Point P is on the bisector of ⦟CAB. Therefore, CP = BP

Textbook, page 159Patty Paper InvestigationInvestigation 1: Angle Bisecting by folding

Textbook, page 160Investigation 2: Angle Bisecting with compass

You Tube: Constructing an angle bisector

https://www.youtube.com/watch?v=2lP1NKYLKQw

Homework:Draw an obtuse angle.Construct the angle bisector.Describe each step.

3.5: Constructing Parallel Lines

Intersecting lines

Intersecting lines

Parallel lines ?

How would you check whethertwo lines are parallel?

One way is to draw a transversal and compare corresponding angles

Textbook, page 163Patty Paper InvestigationInvestigation : Constructing parallel lines by folding.

You Tube: Constructing parallel lines usingcorresponding angles.

https://www.youtube.com/watch?v=im81vHIhZS8

https://www.youtube.com/watch?v=JI9IcdLI8WU

Homework:Draw a line and a pointnot on the line.Construct a line through the givenpoint parallel to the given line. Describe each step.