Chapter 1 Slides

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Chapter 1 Slides
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1.2 Points, Lines, and Planes (2 days)
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A definition uses known words to describe a new
word. In geometry, points, lines, and planes are
undefined terms.
Point. Technically, it has no size, but we use a
dot that has size to represent it. You use a
capital letter to label it. Such as Point A
All figures are made of points. This is a LINE.
It goes both ways, forever without ending. Once
again, it has no thickness, but we use a picture
with thickness to describe it. Arrows on both
ends say it goes on forever.
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PLANE, goes on forever, once again has no
thickness. Even though it goes on forever, we
usually use a parallelogram shape to draw it.
A
K
I
M
To label it, a capital cursive letter can be
used, or you can use three points that dont line
up (also known as non-collinear points)
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Collinear points, points all in one line.
Noncollinear points, points NOT all in one line.
Coplanar points, points all in one plane.
Noncoplanar points, points NOT all in one plane.
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Name all the coplanar points.
B
A
C
D
E
F
H
G
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This is a ray
This is a line segment, it is a segment, or part
of a line
T, R are ENDPOINTS
ORDER MATTERS
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OPPOSITE RAYS are called opposite rays cuz N
is between M and O.
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Name four coplanar points
l
ABCD or FGHI or some other combination that works
P
B
Name three collinear points
A
DAB or AEF or GFJ
D
C
What is the intersection of line l and plane P?
E
Point A
Q
G
I
Which plane has points F,H,I?
F
J
H
Plane Q
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• Two or more geometric figures intersect if they
  have one or more points in common. The
  intersection of the figures is the set of points
  the figures have in common.

Draw three noncollinear points A, B, C on plane
P. Draw line l not on plane P going through
point C.
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Draw three planes M, N, P meeting at point P.
Draw three planes M, N, P meeting on line l.
In 3-D, sometimes it helps to imagine a box, or
look around the room (but not during a test)
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1.3 Segments and Their Measures (1 day)
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Postulate \ Axiom A rule that is accepted
WITHOUT PROOF.
Postulate 1 Ruler Postulate The points on a
line can be matched one to one with the real
numbers. The real number that corresponds to a
point is the coordinate of the point. The
distance between points A and B, written as AB,
is the absolute value of the difference between
the coordinates of A and B. AB is also called the
length of AB.
A
B
-1
0
1
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Find the distance between the points
Order of subtraction doesnt matter. But doing
right minus left keeps things positive.
Where your ruler is doesnt matter. Two points
are the same distance apart no matter how you
line up the ruler.
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SEGMENT ADDITION POSTULATE If B is BETWEEN A and
C, then AB BC AC. Also If AB BC AC, then
B is between A and C
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DS 30 DU 5 KS 7 UC .5CK
UK UC DC US
boardwork
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(x2,y2)
(3,2)
(x1,y1)
(-4,-2)
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(-5, -2) (4, 1) x1 y1 x2 y2
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Congruence is shown with marks. The marks say
that they are the same size and shape
Equals means they have equal length, number value.
They are equivalent. Definition of congruent
segments Congruent segments have equal lengths
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Find the distance between Mr. Kim and each food
location.
(0, 12)
(8, 6)
(0, 0)
(16, 0)
(8, 0)
From where Mr. Kim starts, if he goes to
In-N-Out, Der Veener, and Carls, and back to
where he started, how far does he walk?
Does the King scare you too?
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1.4 Angles and Their Measures (2 days)
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L
A
E
N
1
G
S
Angles are formed by two rays with the same
initial point.
Two rays are called the sides.
The initial point is called the vertex
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If two angles are congruent, their measures are
equal. If the measure of two angles are equal,
they are congruent
D
R
1
2
U
E
C
X
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Protractor Postulate
A
O
B
Consider a point A on one side of OB. The rays
of the form OA can be matched one to one with the
real numbers from 0 to 180. The measure of AOB
is equal to the absolute value of the difference
between the real numbers for OA and OB.
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Acute Angle is between 0 and 90 degrees
Right Angle is exactly 90 degrees
Obtuse Angle is between 90 and 180 degrees
90
Straight Angle is 180 degrees
0
180
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• A point is in the interior of an angle if it is
  between points that lie on each side of the
  angle.
• A points is in the exterior of an angle if it is
  not on the angle or its interior

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Adjacent angles, share common side and vertex,
but share NO interior points.
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C
O
B
A
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Find the measure of the unknown angles, state if
they are acute, right, or obtuse.
1
76o
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Draw angle ABC that is 90o. Draw right angle DBF
so that angle ABF and DBA is 45o and A is in the
interior of angle DBF and F is in the interior of
angle ABC.
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• Draw a right angle KIM. Draw angle JIQ such that
  M is in the interior of angle JIQ and Q is in the
  interior of KIM and JIM is 30 degrees and MIQ is
  60 degrees

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1.5 Segment and Angle Bisectors (2 days)
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D
B
A
C
E
SEGMENT BISECTOR A line, segment, or ray that
INTERSECTS THE SEGMENT AT THE MIDPOINT!
The MIDPOINT of a segment divides the segment
into TWO congruent parts.
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What coordinate is in the MIDDLE of these two
points?
(-3, -2) (5, -1) x1 y1 x2 y2
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Find the midpoint.
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Given an endpoint and the midpoint, find the
other endpoint. A is an endpoint, M is a midpoint
A (5, -2) M (3, 6) B (x, y)
A (2, 6) M (-1, 4) B (x, y)
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ANGLE BISECTOR is a ray that divides an angle
into two adjacent angles that are congruent.
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Constructing a perpendicular bisector.
1) Point on one end, arc up and down.
2) Switch ends and do the same
3) Draw line through intersection
This is DIFFERENT from book (slightly).
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Bisect an angle
1) Draw an arc going across both sides of the
angle.
2) Put point on one intersection, pencil on
other, draw an arc so that it goes past at least
the middle.
3) Flip it around and to the same.
4) Line from vertex to intersection.
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1.7 Introduction to Perimeter, Circumference,
and Area
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Square A s2 P 4s
s
Rectangle A lw P 2l2w
l
w
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Circumference is the distance around the circle.
(Like perimeter) C pd 2pr
LIKE THE CRUST PIZZA PART
Area of a circle A pr2
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Fake sun has a radius of .5 centimeters. Find the
circumference and area of fake sun.
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Find Perimeter\Circumference, and Area for each
shape
13 cm
15 cm
5 ft
Scale
12 cm
14 cm
3 ft
3 ft
3 in
6 ft
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Find the area and perimeter
12 cm
17 cm
8 cm
8 cm
12 cm
15 cm
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Find the area of the figure described
Find the area of a circle with diameter 10 m
Find the area of a rectangle with base 4 ft and
height 2 ft
Find the area of a triangle with base 2 in and
height 6 in
Find the area of a square with perimeter 8 miles
Write on board
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Finding Area
Area of triangle with vertices (-1,2) (4,2) and
(2, -2)
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Mr. Kim needs to make a moat around his castle.
The radius of the outer circle is 50 feet, the
radius of the inner circle is 40 feet. What is
the area of his moat?
How many square yards of flooring are needed to
cover a room that is 18 ft by 21 ft?