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Geometry Journal
Michelle Habie 9-3
Point, Line, Plane
Point: A mark or dot that indicates a
location.
Ex:
Line: A straight collection of dots that go on
forever.
Ex:
Plane: Flat surface that extends forever.
Ex:
Collinear Points & Coplanar Points:
Collinear Points:
Points that are in the same line.
Ex:
Non collinear Points:
Points that are not in the same line.
Ex:
Coplanar Points: Points that are on the same plane.
Ex:
This is an
example of
coplanar
points that
are not
collinear.
This 3 points
are coplanar
and
collinear.
Line, Segment, Ray
Line: A straight collection of dots that go on forever.
Ex:
Segment: A line that has a beginning and an end.
Ex:
Ray: A line that has a starting point and in one side it
keeps on going forever and in the other side, it stops.
Ex:
The three of
them join two
points
however, some
stop and other
continues their
path.
What is an intersection?
Intersection:
The point where a line crosses the x axis or the y axis.
Passing across each other at exactly one point.
Exmples:
1.
2.
3.
Real Life
Intersection
Postulate, Axiom, Theorem:
Difference:
Postulate:
A
statement
that is
accepted
as true
without
proof.
Axiom:
A
statement
that is
accepted
as true
without
proof.
Theorem:
A
statement
that has
been
proven.
Ruler Postulate:
To measure any segment you use a ruler and subtract
the values at the
end points.
Use the
ruler
Examples:
postulate
1.
to find
5
8
the
2.
distance
from one
A
B
3.
point to
the
other.
Base
1
Base
2
Segment Addition Postulate:
If A,B and C are 3 collinear points and B is
between A and C then AB+BC=AC.
Examples:
A
B
C
1
Home
2
Vista
Hermo
sa
Blvd.
3
CAG
Use this
postulate to
find the
distant
between 3
or more
points on a
segment.
Distance between 2 points:
To find the distance between two points you use the
distance formula:
√(x2-x1)⌃2+(y2-y1)⌃2
Examples:
1. (2,4) (-1,0)
D=√(2+1)⌃2+(4-0)⌃2=
D=5
2. (3,-2) (6,-8)
D=√(3-6)⌃2+(-2+8)⌃2=
D=√45
3. (1,0) (-2,8)
D=√(1=2)⌃2+(0-8)⌃2=
D=√73
Congruent – Equal:
=
Two things
that have the
same value.
We have to
know the
value
Comparing
Values
AB=3.2
≅
Two things that
have equal
measure.
Might not know
what the value is.
Comparing
Names.
--≅-AB CD
A, B are congruent
and equal.
While B, C are
congruent but, not
equal.
Examples:
A
B
C
Pythagorean Theorem:
The sum of the legs to the squared has to be equal
to the hipothenuse to the square.
Examples:
a2+ b2=c2
A=10 c=16
If a=10 and b=12
Find b
Find c:
b=√16⌃2-10⌃2
2
+
2
c=√(10 ) (12 )
B=√256-100 = b=√156
C=√244
B=8 c=10
Find a
A=√10⌃2-8⌃2
A=√100-64
A=√36=6
Angles and types of angles:
An angle is the joining of two rays with a common point called vertex.
We measure the angles by the distance from ray to ray, we measure them in
degrees.
1. Acute angle (measures 0°-89°)
2. Right angle (measures exactly 90°)
3. Obtuse angle (measures between 91°-179°)
4. Straight angle (measures exactly 180°)
The parts of an
angle are its legs
and the vertex.
Legs
Interior
Legs
Vertex
Angle addition Postulate:
The measurement of two included angles is
equal to the measurement of the whole angle
that includes both.
<CAD+<CAB=<BAD
1. m<CAD= 30° m<CAB=20°
Find m<BAD
m<BAD=30°+20°=50°
B
15°
2. m<BAD= 75° and m<CAD=
C
Find m< CAB
m<CAB=75°-15°=60°
A
D
E
F
3. <EIF=32°, <FIG=40°,
<GIH=38°
Find m<EIH
m<EIH=32°+40°+38°=110°
G
H
Midpoint
The midpoint is the point that bisects a
segment in two congruent parts.
You can find a midpoint by measuring or
using a straight edge( compass).
Examples:
1.
F
E
A
B
is the midpoint
Because lies in the
middle
of segment A,C.
C
The apple
balances this
scale
because it
represents
the midpoint.
If EF= 10
and FG= 9,
then F is
NOT the
midpoint of
EG.
G
Angle Bisector:
It means to divide an angle into two
congruent angles.
To construct an angle
bisector you use a
compass and a ruler
to find it.
Example 1:
Adjacent,Vertical, Linear Pairs of
Angles:
Adjacent: Have a common vertex sharing a ray with no
common interior points.
Vertical: Two non adjacent angles form by two intersecting
lines.
Linear: Adjacent angles with non common sides are opposite
rays.
Supplementary & Complementary
Angles:
Supplementary
:
Any two angles
that add up to
180°
Complementary
:
Any two angles
that add up to
90°
Area and Perimeter of Shapes:
A= s⌃ 2
P= 4s
Example 1 : s=5in
A=(5)⌃2=25in ⌃2
P=4×5=20in
Example 2: s=3cm
A=(3)⌃2=9cm⌃2
P=4×3=12 cm
A= l w
P= 2l + 2w
Example 1 : l= 2 cm, w= 1
cm
A = 2×1=2cm ⌃2
P =2(2)+ 2(1)=6cm
Example 2:l= 5 ft, w=3ft
A= 5×3=15ft⌃2
P= 2(5)+ 2(3)= 16ft
A= ½ l h
L= a+b+c
Example 1 : l= 5, w= 3, b=4, c=6
A = 5×3÷2= 7.5 u ⌃2
L = 5+4+6= 15u
Example 2:l=7, w=4, b=2, c=5
A= 7×4÷2= 14u ⌃2
L=7+2+5= 14u
Area and Circumference of a Circle
Area= π r ⌃2
Example 1:
r= 6
A(3.14)(6)⌃2
A=3.14×36
A=112.04u⌃2
Circumference: 2π r
Example 1:
r= 8cm
c= 2(3.14)(8)
c= 50.24cm
5 Step Process:
If three cans of soda cost $10.50. How much
would seven
cans of soda cost?
1. Read it carefully.
2. Understand the problem
3. Make a plan- I definetly need to set up a proportion.
4. 3 cans=7 cans
------ = ------ = 10.50 ×7
10.50 x -----------3
x=$24.50
5. Look Back if the answer makes sense.
Rotate
Reflect
Translate
Transformations:
Make a copy of a figure in a different
position. A transformation can enlarge an
object or shrink an object.
Examples:
Bibliography:
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http://primaryhomeworkhelp.co.uk/time/pm.gif
http://gmat4all.com/diagrams/a1a.jpeg
http://www.bced.gov.bc.ca/irp/mathk7/icons/f6.gif
http://www.gogeometry.com/heron/angle_bisector.gif
http://content.tutorvista.com/maths/content/geometry/lines%20angl
es%20triangles/images/img61.gif
http://www.freemathhelp.com/images/lessons/angles5.gif
http://2000clicks.com/MathHelp/GeometryTheoremsLinearPair.gif
http://www.analyzemath.com/Geometry/angle_5.gif
http://www.gltech.org/library/April_geometry/supplementary2.gif
http://image.wistatutor.com/content/feed/tvcs/translation_0.jpg
http://image.wistatutor.com/content/feed/u1856/reflection.GIF
http://www.mathsisfun.com/geometry/images/rotation-2d.gif