Transcript File

Classic Constructions
• Ryan Caliguri – WMHS
• Jeffrey Wainz - WMHS
G.SR.07.02
• G- Geometry
• SR- Spatial Reasoning and
geometric modeling
• 07- 7th grade curriculum
• 02- The second type of concept in
that section
G.SR.07.02
• Terminology
• Informal justifications
G.SR.07.02
• Basic Geometric Constructions
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Perpendicular Bisector
Equilateral Triangle
Angle Bisector
Inscribed Circle
Circumscribed Circle
Terminology
Compass: an
adjustable device
used to construct
circles
Straight Edge: any
tool that is used to
draw straight lines
during
constructions
Terminology
Bisector: line
that divides a
segment or angle
into two equal
halves
Perpendicular:
lines that
intersect at 90
degree angles
Terminology
Equilateral
Triangle: triangle
with 3 congruent
sides and angles
Circumscribed
Circle: a circle
drawn around a
triangle
Terminology
Vertex: the point
where two lines
intersect to form
an angle
Inscribed Circle: a
circle drawn
inside of a
triangle
Terminology
Line: a figure that
goes on forever in
2 directions
Line Segment: a
line with a
defined length
Terminology
Ray: a figure that
goes on forever in
one direction and
ends in a point on
the other
Radius: a line that
goes from the
center of the circle
to the outside
Perpendicular Bisectors
• Cuts a line in half
• New line is perpendicular to the
original segment
Constructing a
Perpendicular Bisector
Angle Bisectors
• Cuts an angle in half
• Two new created angles are
congruent
Constructing Angle Bisectors
Equilateral Triangle
• A triangle with sides of exactly the
same side
• All angles are 60 degrees
Constructing Equilateral
Triangles
Inscribed Circle
• Creates a circle using angle
bisectors
• The circle touches all three sides of
the triangle
Inscribed Circle
• Prerequisites
– Angle bisectors
– Perpendicular lines through a point
Inscribed Circle
Circumscribed Circle
• Creates a circle using
perpendicular bisectors
• The circle touches the vertexes of
the triangle
Circumscribed Circle
Where will this be used?
• Architectural design
• Surveying
• Crafts
Where will this be used?
Where is all of this used?
http://www.clker.com/clipart-25627.html
Conclusion
Tools:
• Compass
• Straightedge
• Pencil
Conclusion
• Angles and lines can be bisected
with
– Circles
– Lines
– Points
Work Cited
• http://www.daviddarling.info/ency
clopedia/C/compasses.html
• http://www.theofficedealer.com/A
CM45012-Westcott-45012-Shatterproof-Ruler.html
• http://inefalon.info/staedtler55600-comfort-compass-set.php
• http://www.clker.com/clipart25627.html
MMSTC
Works Cited
• https://commons.wikimedia.org/wi
ki/File:Green_equilateral_triangle
_point_up.svg
• http://en.wikipedia.org/wiki/Circu
mscribed_circle
• http://www.mathwords.com/i/inscr
ibed_circle.htm
ANY
QUESTIONS?
The Game!
• 2 players
• Whoever says the correct letter
first wins- click “Answer” to get the
correct answer
• Correct answers receive one point
unless otherwise specified
MMSTC
Question 1
• An angle is given, what is the first
step in making it’s bisector?
• ( Where does the circle get
placed?)
Go To Diagram!!!
A
B
C
What’s the answer?
Answer
Question 2
• When two lines intersect, and a
circle has been constructed,
radiating from the intersection
point, where does the compass
needle go for the next step?
Go To Diagram!!!
MMSTC
C
A
B
What’s the answer?
Answer
Question 3
• Once one circle is constructed on
the first circle’s intersection with
the angle’s line, how big should you
make the next one and where
should it go?
Go To Diagram!!!
4”
C
A
B
4”
4”
What’s the answer?
8”
Answer
Question 4
• When making a perpendicular
bisector, where would you place
the first circle?
Go To Diagram!!!
A
B
C
What’s the answer?
Answer
Question 5
• After one circle has been created,
beginning the creation of a
perpendicular bisector, what would
be the next step?
Go To Diagram!!!
A
B
C
What’s the answer?
Answer
Question 6
• With two circles constructed, of
equal size over both ends of the
segment, what is the next
construction to be made?
Go To Diagram!!!
B
A
C
What’s the answer?
Answer
Question 7
• When creating an equilateral
triangle, what is the first
construction made on a segment?
Go To Diagram!!!
A
B
C
What’s the answer?
Answer
Question 8
• In the creation of an equilateral
triangle, after a circle is created
around a given point, what size
should the next circle be?
Go To Diagram!!!
B
4”
A C
2”
4”
8”
What’s the answer?
Answer
Question 9
• With two points of an equilateral
triangle discovered, where does
the third go?
Go To Diagram!!!
B
C
A
What’s the answer?
Answer