[OTCQ questions ] Your answer . . . .

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OTCQ: Write this as your first page of notes. All tests until the Regents are open notes, so don’t miss any.
[OTCQ questions ]
Your answer . . . .
Date
9/9/09
Aim
Hwk p
1.1 What is an undefined term? How do we 1.1 What is an undefined term? How do we define a set, point, line and plane? define a set, point, line and plane?
[Continue with ppt notes and examples][Continue with ppt notes and examples][Expect 510 pages of notes every day, min][Expect 510 pages of notes every day, min]
Aim 1.1 What is an Undefined Term? How do we define a Set, Point, Line and Plane?Homework read chapter 11complete problems 311 on page 3.rreidymath.wikispaces.com is my website. All in class powerpoints are posted there so that your notebook may always be up to date.
OBJECTIVES
• SWBAT to define an undefined term.
• SWBAT differentiate an undefined terms from a defined term.
• SWBAT sketch pictures that represent defined terms and undefined terms.
[do not write]NYS Performance Indicatorsfor 1.1Students will use the language of mathematics to express mathematical ideas precisely.
G.CM.10 Use correct mathematical language in developing mathematical questions that elicit, extend, or challenge other students’ conjectures
G.CM.12 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing
What is an undefined term?
In Geometry there are 4 undefined terms
set,
point,
line
plane.
set, point, line & plane
the undefined terms
We say these are undefined because we need to assume their meanings in order to use them to define other things.
Undefined terms
Meanings are assumedAt the start of geometry
Defined terms
Meanings are based on the Undefined terms.
Vs.
set, point, line & plane
the undefined terms
Compare geometry to a game.
Can you explain how rules have to be agreed on up front so that a game may begin?
Definitions of the Undefined terms
SET: A set is a collection of objects defined so that it is possible to say whether an item is in the set or not.
Example: The Yankees are a set.
Derek Jeter was in this set in 2009.
Jose Reyes was not in this set in 2009.
Definitions of the Undefined terms
Point:
A point indicates a location. A point has no width or dimension.
A point is usually represented by a small dot.
A
Point A
Line:
A line is a set of points. A line may be curved or straight.
A straight line includes two arrowheads to indicate that the line extends without end in two directions.
A
B
l
Line l or AB
Definitions of the Undefined terms
Plane:
A plane is a set of points that form a flat surface that extends infinitely in two dimensions.
A plane usually represented by a shape that looks like a tabletop or wall.
A plane extends without end even though the drawing of a plane appears to have edges.
A
BC
M
Plane M or plane ABC
Definitions of the Undefined terms
Next: defined terms. (ie terms based on the undefined terms )• Collinear points are points that lie on the
same line.
• Coplanar points are points that lie on the same plane.
Ex. 1: Naming Collinear and Coplanar Pointsa. Name three points
that are collinear
Solution:
D, E and F lie on the same line, so they are collinear.
G
D E F
H
Ex. 1: Naming Collinear and Coplanar Pointsb. Name four points that
are coplanar.
Solution:
D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn.
G
D E F
H
Ex. 1: Naming Collinear and Coplanar Pointsc. Name three points
that are not collinear.
Solution: There are many correct
answers. For instance, points H, E, and G do not lie on the same line.
G
D E F
H
• The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. Line AB
A
A
B
B
Line segment AB
Next: line segment vs. line
More . . .
• The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie in the same direction from A as point B.
l
Line l or AB
A
A
B
B
Ray AB
More . . .
• Note that AB is the same as BA and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions.
l
Line l or AB
A
A
B
B
Ray BA
More . . . • If C is between A and B,
then CA and CB are opposite rays.
• Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane.
l
Line l or AB
A
C
B
Ex. 2: Drawing lines, segments and rays
• Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.
J
K
L
Draw J, K and L
Then draw JK
Ex. 2: Drawing lines, segments and rays
• Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.
J
K
L
Draw KL
Ex. 2: Drawing lines, segments and rays
• Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.
J
K
L
Draw LJ
Ex. 3: Drawing Opposite Rays
• Draw two lines. Label points on the lines and name two pairs of opposite rays.
Solution: Points M, N, and
X are collinear and X is
between M and N. So
XM and XN are opposite
rays.
P
MQ
N
X
Ex. 3: Drawing Opposite Rays
• Draw two lines. Label points on the lines and name two pairs of opposite rays.
Solution: Points P, Q, and
X are collinear and X is
between P and Q. So XP
and XQ are opposite
rays.
P
MQ
N
X
Ex. 4: Sketching intersection of a plane and a line.• Sketch the figure
described.a. A line that intersects a
plane in one point Draw a plane and a
line. Emphasize the point
where they meet. Dashes indicate
where the line is hidden by the plane
Ex. 4: Sketching intersection of 2 planes.• Sketch the figure
described.
b. Two planes that intersect in a line
Draw two planes. Emphasize the line
where they meet. Dashes indicate where
one plane is hidden by the other plane.
View Homework p.3 problems 3 11
• The Geometry text is available at
www.harborfieldscsd.net/
And
http://www.harborfieldscsd.net/pdf/HS/textbook/Geometry.pdf
ALL HOMEWORK GOES IN THE BACK OF YOUR NOTEBOOK!