Download M2 1st geo journal

Sergio Rivera 9-3
Geometry 1st journal
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____(0-10 pts.) Compare and contrast collinear points with coplanar points. Give an example and a counterexample of each.
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____(0-10 pts.) Explain what a line, segment, and ray are, and explain how they are related to each other. Give an example of each.
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____(0-10 pts.) Describe what an intersection is. Give at least 3 examples.
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____(0-10 pts.) Explain the difference between a postulate, axiom and theorem.
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____(0-10 pts.) Describe the Ruler Postulate. Give at least 3 examples.
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____(0-10 pts.) Describe the Segment Addition Postulate. Give at least 3 examples.
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____(0-10 pts.) Describe how to find the distance between two points on a coordinate plane. Give at least 3 examples.
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____(0-10 pts.) Describe what congruence is and compare it to equality. Give an example of how they are different. Give an example of how they are similar.
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____(0-10 pts.) Describe the Pythagorean Theorem. Give at least 3 examples.
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____(0-10 pts.) Describe what an angle is and how they are measured. Be sure to include a discussion about the parts of an angle, and the different types of angles. Give an example
of each.
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____(0-10 pts.) Describe the Angle Addition Postulate. Give at least 3 examples.
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____(0-10 pts.) Describe what a midpoint is and how it can be constructed, and how it can be found using the midpoint formula. Give at least 3 examples.
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____(0-10 pts.) Describe what an angle bisector is, and how to construct one. Give an example.
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____(0-10 pts.) Describe what adjacent, vertical and linear pairs of angles are. Give an example of each.
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____(0-10 pts.) Compare and contrast complementary and supplementary angles. Give examples of each.
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____(0-10 pts.) Describe how to find the perimeter and area for the following shapes: square, rectangle and triangle. Give 2 examples of each.
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____(0-10 pts.) Describe how to find the area and circumference of a circle. Give 2 examples.
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____(0-10 pts.) Describe the five-step process for solving any problem you encounter this year. Give an example, clearly showing all five steps.
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_____(0-10pts.) Describe what a transformation is and how they change the original object. Give at least 3 examples.
1.
A point is a dot representing a location, it has no size.
X .
A line is a no thickness straight path that goes on forever.
<------------o--------------o------------->
X
Y
A plane is a flat surface that extends forever and has no
thickness.
http://www.freehomeworkmathhelp.com/Geometry/Geometry_Introduction/geome
try_homework_help_plane_points.GIF
same plane. Something that is similar is that they both are non when
the points don't lie on the same line or plane, also something similar is
that are points indicating that they go on forever.
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Collinear:
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<------------o--------------o------------->
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X
Y
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Noncollinear:
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<------------o--------------o------------->
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X
Y
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o
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M
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Coplanar:
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BCA
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Noncoplanar:
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A line is a straight path and extends forever.
<------------o--------------o------------->
A
B
A segment is a part of a line but it has 2 points and all of the points
are in between it has an end in both sides.
o----------------o
A
B
A ray is part of a line that starts at an endpoint and extends forever in
the other direction.
o--------------------o---->
A
B
They all are similar because each of them are part of a line and have
points inside of it. Just the difference is that each one has endpoints.
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An intersection is the part in which two lines etc, meet.
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• A postulate and axiom are the same
thing. Both are approved things that are
accepted, and a theory is a problem
that you need to prove it with formulas
and geometry graphs
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Ruler Postulate: The points on a line can be put into a one-to-one
correspondence with the real numbers.
<--l----l-------l--l---------l---l--->
A
X
a) AW = 11
b) XY= 18
c) YT = 3
d) XR = 9
W R
each - is 1 cm.
Y
T
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AC=AB+BC
14=AB=11.4
-11.4
-11.4
7
2.6=Ab
ex. 2 S is between R and T. Find RT
RT=RS+ST
4x=(2x+7)=28
4x=2x+35
-2x
-2x
2x=35
/2 /2
x=35/2 or 17.5
RT=4x
4(17.5)=70
ex. 3 B is between A and C, AC=15.8 and AB=9.9. Find BC
AB+BC=AC
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Congruence is two things that have the same measure, or the same
degrees if it is an angle. Equality is the same distance but in another
measure.
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Congruency:
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equal:
1000m = 1 km
3500m = 3.5km
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Pythagorean Theory: a^2+b^2=c^2
in a right triangle, the sum of
the squares, is the length of the legs, is equal to the square of the
hypotenuse
ex 1. a=8 b=4
c=8^2+4^2
c=64=16
c=80
ex. 2. a=3 b=5
c=3^2+5^2
c=9+25
c=34
ex 3. a=10 b =6
c=10^2+6^2
c=100+36
c=136
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• An
angle is a an edge of things, it has rays
that have the same endpoint and then
extend forever. There are 4 types of angles:
Obtuse (more than 90º)
Straight (180º)
Acute (less than 90º) Right angle (exactly 90º)
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• Two or more angles can add up to a
bigger angle.
angle
ABC=120º
angle
QWE=60º
120+60=180º
Angle YUI=132
Angle WER=39
132+39=171º
angle ZXC=23
angle ASD=23
angle GHJ=23
23*3=69
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• The midpoint is the exact middle of a
segment, both sides should have the
same distance.
(2,4),(4,6)
2+4= 6
6/2=3
4+6=10
10/2=5
(3,5)
This is the formula:
X1+X2 , Y1+Y2
2
2
(4,9) (8,3)
4+8=12
12/2=6
9+3=12
12/2=6
(6,6)
(5,7) (3,1)
5+3=8
8/2=4
7+1=8
8/2=4
(4,4)
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• To bisect means to cut in half. To bisect
an angle means to cut an angle in two
equal parts. First yo need to grab a
compass make a arc in each segment.
then from the segment make an arc on
the middle, make it from both
segments. then make a segment from
the two las arcs to the midpont
• 1. Adjacent angles:
15angles that are in
the same plane having a a common
vertex and side.
• 2. Linear pair are angles that share a
common side but the non-common side
is a ray.
1
• 3 .Vertical2 are two lines that3 intersect
and are always congruent.
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• The supplementary angles are angles
that its º ad up to 180º, in the other
side complementary add up to 90º.
they both are angles adding up and
supplementary always make a linear
plane and complementary make up
adjacent.
Supplementary
Complementary
• Square: to find perimeter you need to
add up all sides. to find area multiply
length and width.
• rectangle: to find perimeter you need to
add up all sides, and area multiply
length and width.
• triangle: you should add up a+b+c, and
to find area =1/2bh
examples:
square:
L=4cm W=4cm
perimeter= 16cm
Area=16cm
Rectangle:
L=10 W=5
p=30
a=50
triangle
a=4 b=6 c=2cm
p=12cm
a=6cm
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1
8
• To find the area it is πr^2. To find the
circumference is πd. π=3.14 cm.
Circumference
8*3.14=25.12cm
c=25.12cm
d=8
Area
r=4
(3.14*4)^2
12.56^2
a=157.7536
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• The five steps of how to solve any
1. The length
of a rectangle
is 12 cm and
width is 14.
Find area
problem are the following:
1.Read carefully
2. write any important information
3. Draw a picture to do guide.
4.write equation
5. solve it and answer question.
2. L=12 W=14
4. LW=A
3.
12 cm
14 cm
5. a=168
12 *14=
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• Transformations:
1.
1.reflection: flip of a shape making it
negative.
2.rotation: shape stays the same only
the shape moves and turns.
3.translation: movement of an object.
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