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Objectives: To use inductive reasoning to
make conjectures


Inductive Reasoning  reasoning that is
based on observed patterns. If you see a
pattern or sequence, you can use inductive
reasoning to tell what the next term in the
sequence will be.
Conjecture:  a conclusion reached by using
inductive reasoning.

Ex: Use inductive reasoning to find the next
two terms in each sequence.
3, 6, 12, 24 …
A, B, C, D …
Mon, Tue, Wed …
O, T, T, F, F, S, S …


Not all conjectures turn out to be true. You
can prove that a conjecture is false by finding
one counterexample.
Counterexample  an example for which the
conjecture is incorrect/false.

Ex: Find a counterexample for each
conjecture.
The square of any number is greater than
the original number.
You can connect any three points to form a
triangle.
Any number and its absolute value are
opposites.

Homework Formatting
◦ All homework must be done in pencil. Homework
done in pen will not be accepted.
◦ Write and circle the problem number.
◦ Box your answer.
◦ Attempt every problem even if you are unsure. I will
go over homework questions the next day so make
sure you ask if you have a question. This is
important because many quiz and test questions
will come directly from the homework.
 Homework
#1
 Due Tuesday (Aug 14)
 Page 6 – 7
# 2 – 18 even
#25 – 28 all

Objectives:
To understand basic terms of geometry
To understand basic postulates of
geometry
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
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Point  think of as a location. It has no size.
It is represented by a small dot and is named
by a capital letter.
Space  the set of all points.
Line  a series of points that extends in two
opposite directions without end. You can
name a line by any two points on the line or
with a single lowercase letter.
Collinear points  points that lie on the same
line.
n
C
F
E
P
m
D
r
Name each line.
Are points E, F, and C collinear?
Are points E, F, and D collinear?
Are points F, P, and C collinear?

Plane  a flat surface that has no thickness. A
plane contains many lines and extends
without end in the directions of all its lines.
◦ Planes are named by either a single capital letter or
by at least three of on its non-collinear points.

Coplanar  points and lines that lie in the
same plane.


Postulate/Axiom  an accepted statement of
fact.
Postulate 1.1
◦ Through any two points there is exactly one line.

Postulate 1.2
◦ If two lines intersect, then they intersect in exactly
one point.

Postulate 1.3
◦ If two planes intersect, then they intersect in exactly
one line.

Postulate 1.4
◦ Through any three non-collinear points there is
exactly one plane.
 Homework
#2
 Due Wednesday (Aug 15)
 Page 19 – 20
◦# 1 – 33 odd

Objectives:
To identify segments and rays
To recognize parallel lines

Segment  the part of a line consisting of
two endpoints and all points between them.
Segment AB
A
endpoint
AB
B
endpoint

Ray  the part of a line consisting of one
endpoint and all the points of the line on one
side of the endpoint.
Ray YX
X
YX
Y
endpoint

Opposite Rays  two collinear rays with the
same endpoint. Opposite rays always form a
line.
Shared endpoint
Q
R
RQ and RS are opposite rays
S

Ex: Name all the segments and rays in the
figure below. Are there any opposite rays?
Q
P
L
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Parallel Lines  coplanar lines that do not
intersect.
Skew Lines  are non-coplanar; therefore,
they are not parallel and do not intersect.
Parallel Planes  planes that do not intersect.
Lines and planes can also be parallel as long
as they do not intersect.

Ex: Identify any parallel lines, parallel planes,
and skew lines in the figure below.
B
C
D
A
F
E
G
H
 Homework
#3
 Due Thursday (Aug 16)
 Page 25 – 26
◦#1- 33 odd
 Quiz
Friday (1.1 – 1.5)

Objectives:
To find the lengths of segments

Postulate 1.5 – Ruler Postulate
◦ The points of a line can be put into one-to-one
correspondence with the real numbers so that the
distance between any two points is the absolute
value of the difference of the corresponding
numbers.
A
B
a
b
Length of AB = 𝑎 − 𝑏

~
Congruent (=) Segments  segments with
the same length. For example, if AB = 2cm
and CD = 2cm then we can say:
~ CD
AB =

Postulate 1.6 – Segment Addition Postulate
◦ If three points A, B, and C are collinear and B is
between A and C, then AB + BC = AC
A
B
AB + BC = AC
C

Ex: EG = 100. Find the value of x. Then find
EF and FG.
4x - 20
E
2x + 30
F
G

Midpoint  a point that divides the segment
into two congruent segments. A midpoint, or
any line, ray, or other segment through a
midpoint, is said to bisect the segment.

Ex: C is the midpoint of AB. Find AC, CB, and
AB.
2x + 1
A
3x - 4
C
B
 Homework
#4
 Due Friday (Aug 17)
 Page 33 – 34
◦# 1 – 19 odd
 Quiz
Tomorrow

Objectives:
To find the measures of angles
To identify special angle pairs

Angle  formed by two rays with the same
endpoint. The rays are the sides of the angle.
The endpoint is the vertex of the angle.
B
vertex
2
T
Q
Can be named: <TBQ, <QBT, <B, or <2

Angles can be classified by their measure
x°
Acute Angle
0 < x < 90
x°
Obtuse Angle
90 < x < 180
x°
Right Angle
X = 90
x°
Straight Angle
X = 180


Congruent Angles  angles with the same
measure.
Postulate 1.8 – Angle Addition Postulate
◦ If point B is in the interior of <AOC, then
m<AOB + m<BOC = m<AOC.
◦ If <AOC is a straight angle, then
m<AOB + m<BOC = 180
B
A
O
C

Some angle pairs have special names.

Vertical Angles  two angles whose sides are
opposite rays.

Adjacent Angles  two coplanar angles with a
common side, a common vertex, and no common
interior points.

Complementary Angles  two angles whose
measures have a sum of 90°

Supplementary Angles  two angles whose
measures have a sum of 180°
 Homework
#5
 Due Tuesday (Aug 21)
 Page 40
◦# 1 – 23 all

Objectives:
To find the distance between two points in
the coordinate plane.
To find the coordinates of the midpoint of
a segment in the coordinate plane.
Quadrant II
(-,+)
Quadrant I
(+,+)
Origin (0,0)
Quadrant III
(-,-)
Quadrant IV
(+,-)

Formula – The Distance Formula
◦ Used to find the distance between two point that
are not on a horizontal or vertical line.
◦ The distance d between two points A(𝑥1 , 𝑦1 ) and
B(𝑥2 , 𝑦2 ) is:
d=
(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2

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Finding the midpoint of a segment in the
coordinate plane is similar to finding the
mean (average) between two values.
Formula – The Midpoint Formula
◦ The coordinates of the midpoint M of AB with
endpoints A(𝑥1 , 𝑦1 ) and B(𝑥2 , 𝑦2 ) are:
M=
𝑥1 + 𝑥2 𝑦1 + 𝑦2
(
,
)
2
2

Ex: Find the distance.
T(5, 2) and R(-4, -1)
A(1, -3) and B(-4, 4)

Find the midpoint.
Q(3, 5) and R(7, -9)
X(2, -5) and Y(6, 13)
 Homework
#6
 Due Wednesday (Aug 22)
 Page 56
◦# 1 – 31 odd

Objectives:
To find perimeters of rectangles and
squares, and circumferences of circles.
To find areas of rectangles, squares, and
circles.
s
s
Square

Perimeter = s + s + s + s -or- P = 4s

Area = s · s -or- A = 𝑠 2
b
h
h
b
Rectangle

Perimeter = b + b + h + h -or- P = 2b + 2h

Area = b · h -or- A = bh
r
d
Circle

Circumference = Πd -or- 2Πr

Area = Π𝑟 2

Ex:
Find the perimeter and area of a square
with side lengths 8cm.
Find the perimeter and area of a rectangle
with base 4m and height 8m.
Find the circumference and area of a circle
with diameter 10mm.

Postulate 1.9
◦ If two figures are congruent, then their areas are
equal.

Postulate 1.10
◦ The area of a region is the sum of the areas of its
non-overlapping parts.
 Homework
#7
 Due Thursday (Aug 23)
 Page 65
◦# 1 – 31 odd