Transcript 3.1 Duplicating segments and angles

3.1 Duplicating Segments and
Angles
“It is only the first step that is difficult”
Marie De Vichy-Chamrod
Objectives
• Introduce geometric constructions with
straightedge, compass, and patty paper.
• Distinguish among construction, sketches, and
drawings of geometric figures.
• Discover construction methods to duplicate a
segment, an angle, and a polygon.
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
sketch
triangle that looks like an equilateral triangle. No geometry tools
needed.
When you ___________
an equilateral triangle with a compass
construct
and straightedge, you don’t rely on measurements from a
protractor or a ruler. This guarantees that you triangle is
equilateral.
Investigation 1
Copying a Segment
Copying a Segment
p 143
Investigation 2
Copying an Angle
p 144
Copying an Angle
3.2 Constructing Perpendicular
Bisectors
“ To be successful, the first thing to
do is to fall in love with your work.”
Sister Mary Lauretta
Objectives
• Discover a method of constructing
perpendicular bisectors and midpoints.
• Make conjectures about perpendicular
bisectors.
Definitions
____________________:
A line, ray, or segment in a plane that
Segment Bisector
passes through the midpoint of a segment in a plane.
Perpendicular
Bisector A line, ray, or segment in a plane that
____________________:
cuts a line segment into two equal parts at 90°.
Median
____________________:
The segment connecting the vertex of
a triangle to the midpoint of its opposite side.
____________________:
The segment that connects the
Midsegment
midpoint of two sides of a triangle.
Investigation 1
Finding the Right Bisector
P. 147
Perpendicular Bisector
Perpendicular Bisector Conjecture
If a point is on the perpendicular bisector of a segment, then it is
equidistant from the endpoints.
____________
Investigation 2
Right Down the Middle
P. 148
Converse of the Perpendicular Bisector Conjecture
If a point is equidistant from the endpoints of a segment, then it is on the
perpendicular bisector
______________________
of the segment.