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Chapter One Quiz
Friday 1/13
Warmup
pg. 1 #11-15
You have 5 minutes to finish the warm up
Please have your homework out
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4
2x = 6
x=3
3x – 12 = 6
3x = 18
x=6
3
2x + 6 – 1 = 7x
5 = 5x
x=1
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What are we learning today?
 Points, lines, planes,
segments, rays
 Collinear and Coplanar
 Intersections
 Segment length
 Distance Formula
 Segment addition
 Segment Bisector
 Midpoint
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3 Undefined Terms
Segments and Rays
A line segment is a part of a line that is bounded by two
distinct endpoints.
A ray, also called a half line, starts at one point and goes
forever in one direction.
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Segments and Rays
Opposite rays are rays that share a starting point and go
forever in opposite directions.
Collinear and Coplanar
Collinear points are points that lie on the same line. 2 points are
always collinear because a line can be drawn between any two
points.
Example: Name 3 collinear points
D, E, and F
Coplanar points are points that lie on the
same plane. 3 points are always coplanar
because a plane can be drawn between any 3
points.
Example: Name 4 coplanar points
D, E, F, and G
or
H, E, F, and D
The points on two intersecting lines are always
coplanar
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Intersections
2 figures intersect if they have one or more points in common
2 lines intersect in
one point
Line MN and line PQ
intersect at point X
One line and one
plane intersect in one
point
2 planes intersect in
one line
Intersecting Planes
What is the intersection of plane MLK and plane KPQ?
Are the points MJPQ coplanar?
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Segment Length
The length of a segment is the absolute value of the difference
between the numerical values assigned to the endpoints of a
segment
Congruent segments are 2 segments that have the same length
Segment Length
Find the length of segment TV
Find the length of segment SV
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Segment Addition
Find PR if PQ = 5 and QR = 17
Solve for y if we know the
following
PQ = 7y + 9
QR = 3y + 4
PR = 143
Classwork
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3
5
8
10+7 = 17
20+22 = 42
25 – 12 = 13
19 – 12 = 7
Definition of a bisector
What is your definition of a bisector?
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Segment Bisector
A segment bisector is a ray, line, segment or plane that
splits a segment into two equal segments
Midpoint
A segment bisector always passes through the midpoint of the segment
that is being bisected.
That means a midpoint always divides a segment into 2 equal parts.
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Midpoint
A is the midpoint of segment XY.
find the value of x and then find the length of XA and AY
Assignment #2
pg. 16-17
#8-14, 28,30,34,36
In the geo book
pg. 23-25
#6-14, 20,24, 35, 39, 40,43
in the geo book
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Chapter One Quiz
Friday 1/13
Warmup
6 minutes to finish
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BD = 7
HI = 23-12 = 11
7+2t-1 = 30
2t+6=30
2t = 24
t = 12
3x = 2x + 2
x=2
LM = 3(2) = 6
LN = 2(6) = 12
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What are we learning today?
 Rays become angles
 Measures of angles
 Classifying angles
 Congruent angles
 Angle addition
 Angle bisector
 Adjacent Angles
 Linear pairs
 Vertical angles
 Complementary and Supplementary angles
Rays Become Angles
If two different rays have the same initial
point they form an angle
You name an angle using 3
letters. Those letters are the
vertex and then one point on
each side of the angle.
If the angle is not touching
any other angles you can use
only the vertex to name the
angle.
CAB or A
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Angle Measure
Angles are measured in degrees and you use a
protractor to measure an angle in real life
Congruent angles are 2 angles that have the
same measure
Classifying Angles
You classify angles by the measure of the angle
1) Acute angle – measure is between
00 and 900
2) Right angle – measure is 900
3) Obtuse angle – measure is
between 900 and 1800
4) Straight angle – measure is 1800
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Angle Measure
mCAE = ?
mBAE = ?
Classwork
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60o
70o
120o
40o
180o
acute
acute
obtuse
obtuse
right
straight
Angle Addition
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Angle Addition
4x – 20 + 3x + 14 = 155
7x – 6 = 155
7x = 161
x = 23
4(23)-20 = 72o
3(23)+14 = 83o
Angle Addition
4x + 10 + 6x - 5 = 175
10x + 5 = 175
10x = 170
x = 17
6(17)-5 = 97o
4(17)+10 = 78o
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Angle Bisector
An angle bisector is a ray that divides
an angle into two congruent adjacent
angles
Angle Bisector
12x – 7 = 5x + 28
7x = 35
x=5
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Classwork
Adjacent Angles
Adjacent angles are 2 angles that share a
side and a vertex
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Linear pair
Adjacent angles formed by 2 intersecting lines create a linear pair.
The sum of a linear pair is always 180o
Vertical Angles
Vertical angles are angles opposite one another at the intersection of two lines.
Vertical angles are congruent.
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Complementary and Supplementary angles
Complementary angles are 2
angles that have a sum of 90o
Supplementary angles are 2
angles that have a sum of 180o
Examples
Find the value of x and y
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Assignment #3
pg. 31-33 #6-23,30, 32,44-49
pg. 38-40 #8-20even,
25,28,34,36
Chapter One Quiz
Friday 1/13
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Warmup
A
H
B
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H
A
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What are we learning today?
 Midpoint
 Distance Formula
 Perimeter
 Circumference
 Area
Midpoint
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Distance Formula
Classwork
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Perimeter
The perimeter of an object is the distance around the outside of
the object. If you know the length of every side of the object you
can find the perimeter by finding the sum of the side lengths.
Circumference
The perimeter of a circle is called the circumference. To find the
circumference of a circle you must use the following formula.
C = πd or C = 2πr
where d is the diameter
and r is the radius
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Area
The area of an object is the total number of square units the object
contains. To find the area of an object you must know the proper
area formula for each object.
Area Examples
Find the area and the circumference of the circle. Leave
answers in terms of π.
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Area Examples
Area Examples
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Assignment #4
pg. 64-66 #8,10,18,24,
33,39,44-46
in the geo. book
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