Download STUDY OF THE LINE: THE PERPENDICULAR BISECTOR

Geometry I
STUDY OF THE LINE:
THE PERPENDICULAR BISECTOR
Study of the Line, Second Series:
The Perpendicular Bisector (B4: 20)
Material
Geometry Classified Nomenclature B4 (20)
Paper
Pencil
Compass
Ruler
Presentation
(See page 106 for detailed instructions.)
1.
Lay out the geometry classified nomenclature card B4 (20) on the work
area.
2.
Read the definition and match it to the picture. (Latin: ‘bi’ - two, ‘sector’ cutter)
B20
The perpendicular bisector of a line segment is a perpendicular line
drawn through the midpoint of a line segment.
3.
Share the Second Series B4 booklet with the children.
4.
Display the Second Series B4 wall chart.
NOTE: It is suggested that the perpendicular bisector follow perpendicular lines.
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Geometry I
B20
Perpendicular Bisector
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Geometry I
TO COPY A LINE SEGMENT
1
3
Objective: Copy Line Segment AB
A
A
B
B
C
Draw a Segment longer than AB
2
A
B
Place a compass tips on A and B.
4
C
Establish a point ( C ) on the
longer line that
corresponds with A ON AB.
A
B
C
D
With metal tip at C, transfer
length of AB to longer line.
label D CD=AB.
TO CONSTRUCT A PERPENDICULAR TO A LINE FROM A POINT OFF THE LINE
Objective: Construct a perpendicular
to AB passing through C.
c
A
A
c
2
B
H
xD
Draw a segment longer than AB.
c
1
A
H
I
B
Using C as A
center and any
convenient
length as A
radius, draw an
Arc which
intersects AB
at two points
(H and I).
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I
B
c
2
A
H
Using points H
and I as
centers, draw
arcs with
equal radii
that intersect
at a point (D)
below the line.
Draw CD, CD
I
B
xD
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Geometry I
STUDY OF THE LINE:
THE RELATIONSHIP OF THREE
STRAIGHT LINES
Study of the Line, Second Series:
The Relationship of Three Straight Lines (B5: 21 - 23)
Material
Geometry Stick Box
Geometry Classified Nomenclature B5 (21 - 23)
Paper
Red and blue pencils
Presentation
1.
Place paper on the board.
2.
Take two sticks and tack them to the board. Note that these lines are not
parallel and that they actually go on to infinity at both ends. The sticks are
only representations of the line. The paper is the plane and both straight
lines are on the plane.
3.
The plane is subdivided by these lines into three parts. Color the outer parts
of the plane red and the part lying between the two straight lines blue.
4.
Name the outer regions exterior and the inner regions interior. The colors
help to point out the concept of interior and exterior regions.
Exterior Region
Interior Region
Exterior Region
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Geometry I
5.
Take a third stick with holes all along its length.
6.
Place this stick on the first two and give the term transversal. (Latin:
traversare - to cross.)
7.
Determine how many angles are formed: Place a yellow pen mark at each
angle.
8.
Establish which are the exterior angles and which are the interior angles.
A) Those which lie on the external part are exterior angles. External
means outside - in this case outside the two lines. Mark these angles
with red tacks.
B)
Those which lie in the internal part are interior angles. Internal means
inside - in this case, inside the two lines. Mark these angles with blue
tacks.
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Geometry I
9.
Lay out the geometry classified nomenclature cards B5 (21 - 23) from left to
right at the top of the work area.
10. Distribute the labels to the children.
11. Invite each child to read the label and to match it to the picture.
12. Distribute the definitions. Invite each child to read the definition and to
match it to the picture.
B21
Two straight lines divide the plane into three regions. The interior
region is the region that lies between the straight lines.
B22
Two straight lines divide the plane into three regions. The exterior regions are the two regions that do not lie between the straight lines.
B23
The transversal line is a line that intersects two or more straight
lines.
13. Share the Second Series B5 booklet with the children.
14. Display the Second Series B5 wall chart.
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Geometry I
B21
Interior Region
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B23
B22
Exterior Regions
Transversal Line
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Geometry I
STUDY OF THE ANGLE:
PARTS OF AN ANGLE
Study of the Angle, Third Series:
An Angle, Parts of an Angle (C1: 24 - 27)
Material
Geometry Stick Box
Geometry Classified Nomenclature C1 (24 - 27)
Two sticks with an arrow taped to one end of each
Presentation
1.
Recall that each stick with an arrow fastened to it is a ray.
2.
Fix the two rays together on the plane by tacking their origins together.
3.
Say, “When two rays have the same origin, the figure they form is called an
angle.”
4.
Invite the children to construct angles.
5.
“When two rays form an angle, we can call each of the rays a side of the
angle. Their shared origin is the vertex of the angle. The space between
the sides is called the size of the angle.” Label each part as you define it.
6.
Continue with a three-period lesson.
7.
Lay out the geometry classified nomenclature C1 (24 - 27) at the top of the
work area.
8.
Distribute the labels to the children.
9.
Invite the children to read the label and to match the label to the pictures:
angle, sides, vertex, size.
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Geometry I
10. Then distribute the definitions. Invite the children to read the definitions
and to match the definitions to the pictures.
C24
An angle is a figure formed by two rays drawn from the same origin.
C25
The sides of an angle are two rays which form the angle.
C26
The vertex of the angle is the common origin of two rays.
C27
The size of the angle is the measurement of the opening between the
two rays. The size of the opening is measured in degrees.
11. Share the Third Series C1 booklet with the children.
12. Display the Third Series C1 wall chart.
NOTE: At this point the presentations on measuring angles and the use of the
protractor may be introduced with the lesson on the Sumerians (pp. 187 - 188) or
delayed.
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Geometry I
B14
Angle
B15
Sides of an Angle
B16
Convergent Lines
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B17
Size of the Angle
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Geometry I
STUDY OF THE ANGLE:
TYPES OF ANGLES
Study of the Angle, Third Series:
Types of Angles (C2: 28 - 33)
Material
Geometry Stick Box
A red pencil
A red tack
Geometry Classified Nomenclature C2 (28 - 33)
Presentation
1.
Take two sticks of different lengths (a red stick and a tan stick - the tan stick
having holes all along it.)
2.
Superimpose the longer stick over the shorter stick.
3.
Attach the two sticks to the plane with a red tack that represents the vertex
of the angles that will be formed with the sticks.
4.
Fix the tan stick at the other end also, but leave the red stick free.
5.
Take a red pencil and place it in the last hole of the red stick.
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Geometry I
6.
Move the red stick saying, “This is an angle.”
7.
Make the angle wider, saying, “This is an angle.”
8.
Continue to move the red stick around the plane, naming the figure of the
angle each time.
9.
When the rotation is complete, say, “This is a whole angle.”
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Geometry I
10. Illustrate acute angle.
Acute Angle
11. Illustrate right angle.
Right Angle
12. Illustrate obtuse angle.
Obtuse Angle
13. Illustrate straight angle.
Straight Angle
14. Illustrate reflex angle.
Reflex Angle
15. Illustrate whole angle.
NOTE: The measuring angle is used to verify the right angle
Reflex Angle
and to establish acute and obtuse angles.
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Geometry I
16. Use the measuring angle to illustrate the fact that the straight angle is two
measuring angles.
17. Use the measuring angle to illustrate that the whole angle is four measuring
angles.
18. Ask the child to use the sticks to form a right angle, an acute angle, and an
obtuse angle.
19. Lay out the geometry classified nomenclature cards C2 (28 - 33) from left to
right at the top of the work area.
20. Distribute the labels to the children.
21. Invite each child to read the label and to match it to the picture.
22. Then distribute the definitions. Allow each child to read the definition and
to match it to the picture.
C28
The whole angle is formed by one complete rotation of a ray around
its origin.
C29
The straight angle is an angle whose sides extend in opposite directions from its vertex.
C30
The right angle is an angle that is exactly half of a straight angle.
C31
The acute angle is an angle that is smaller than a right angle.
C32
The obtuse angle is an angle that is larger than a right angle and smaller
than a straight angle.
C33
The reflex angle is an angle that is larger than a straight angle and
smaller than a whole angle.
23. Share the Third Series C2 booklet with the children.
24. Display the Third Series C2 wall chart.
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Geometry I
STUDY OF THE ANGLE:
PRINCIPLE ANGLES
Study of the Angle, Third Series: Principle Angles
Material
Geometry Stick Box
White paper
Presentation - Length versus Size of an Angle
1.
Place one sheet of paper on the geometry stick board. Take two sticks of
different lengths, the longer with holes all along it.
2.
Superimpose the longer one over the shorter. Attach the two sticks to the
plane with a long pin, representing the vertex of the angle formed. Fasten
the shorter stick at its other end also.
3.
Place the red pencil through the third hole of the longer stick, and show the
formation of the various angles.
4.
Make an acute angle. Move the stick slowly, and ask the child to tell you
when it forms a right angle. As each angle is formed, name it, mark it, and
label it on the paper.
5.
Ask the child to tell you when it forms an obtuse angle.
6.
Ask the child to tell you when it forms a straight angle.
7.
Ask the child to tell you when it forms a reflex angle.
8.
Ask the child to tell you when it forms a whole angle.
9.
Move it down two more holes and repeat the procedure. In this way, we demonstrate the fact that the size of the angle does not depend on the length of the
sides. The sides become longer, but the size of the angle remains the same.
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