Topic 1 Chapter 3: Constructions Greek philosopher Plato Euclid(Elements) 1. Duplicating (copying) a segment 2. Duplicating (copying) an angle 3. 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 segment 6. 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 on the line
1.(3.2)Constructing Perpendicular bisectors 2.(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 lines the 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 149 Patty Paper Investigation Investigation 1: Finding the right bisector Textbook, page 150 Investigation 2: Constructing the Perpendicular bisector You Tube: Constructing the perpendicular bisector https://www.youtube.com/watch?v=xxi60b3m70y
Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints. If Line AC is the Perpendicular bisector of Segment PQ, then BP=BQ
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, then Line AC is the Perpendicular bisector of Segment PQ.
Homework: Workbook 3.2 Exercise 1. Describe each step
3.3: Constructing Perpendiculars to a Line The distance from point P to line AS is the length of segment PM. Shortest Distance Theorem: The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.
Textbook, page 154 Patty Paper Investigation Investigation 1: Finding the Right Line Textbook, page 155 Investigation 2: Patty-Paper Perpendiculars You Tube: Constructing the perpendicular bisector https://www.youtube.com/watch?v=i4dh2r6b1n0
Homework: Draw a line and a point not on the line. Construct the perpendicular from that point to that line. Describe each step.
3.4: Constructing Angle Bisectors
Point P is on the bisector of CAB. Therefore, CP = BP
Textbook, page 159 Patty Paper Investigation Investigation 1: Angle Bisecting by folding Textbook, page 160 Investigation 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 whether two lines are parallel? One way is to draw a transversal and compare corresponding angles
Textbook, page 163 Patty Paper Investigation Investigation : Constructing parallel lines by folding. You Tube: Constructing parallel lines using corresponding angles. https://www.youtube.com/watch?v=im81vhihzs8 https://www.youtube.com/watch?v=ji9icdli8wu
Homework: Draw a line and a point not on the line. Construct a line through the given point parallel to the given line. Describe each step.