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Geometry 1
Unit 1:
Basics of Geometry
August
Monday
Tuesday
4
Wednesday
Thursday
5 1st Day of Classes 6
8
7
Freshman First Day 1.1 Patterns and
1.2 Points Lines and
Inductive Reasoning Planes
1.3 Segments and
Their Measures
Homework: Patterns
notebook pages 5-6 Page 13 #10-42 even,
#44- 47 all
Page 21 #20-42 even
15
12
13 Meet Your Teacher 14
11
Review 1.1-1.3
Friday
1.4 Angles and Their 1.4 Angles and Their
1.5 Segment and
Measures
Measures
Using Algebra Review Angle Bisectors
Page 8 #34-41 all,
page 15 #56-66
Page 30 #26-40
even, page 23 #46- page 29 #1-8 all, #12- even, Page 31 #50- Page 790 #1-34 1st Pages 38-40 #22-30
54 even
22 even
53 all
column only.
even, #38-48 even
18
19
20
21
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1.6 Angle Pair
Relationships
1.7 Introduction to
Perimeter,
Circumference, and
Area
Page 47-48 #8 - 36
even page 49 #48
and 50
Page 55 #10-26
even, Page 57 #4148 all
Review Unit 1
Review Unit 1
Geometry 1
Chapter 1 Basics of
Geometry Exam
STUDY
Page 63 #1-22 all
1
1. Create your own pattern using numbers. Describe the rule for your pattern.
2. Create your own pattern using pictures. Describe the rule for your pattern.
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Geometry 1
1.1 Patterns and Inductive Reasoning
Unit 1: Basics of Geometry
Example 1
Describe how to sketch the fourth figure in the pattern.
Then sketch the fourth figure.
Figure 4
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Figure 5
Example 2
Describe the pattern in the numbers –7, –21, –63, –189,…
Write the next three numbers in the pattern
Describe the pattern in the numbers 5.01, 5.03, 5.05, 5.07,…
Write the next three numbers in the pattern.
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4
5
1. Write two conjectures that are true. Give examples to support your conjectures.
2. Write 2 conjectures that are false. Write a counterexample for each conjecture.
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Conjecture
Inductive Reasoning
Example 3
Number of Points
1
2
3
4
5
Pictures
Number of Connections
Conjecture:
Example 4
Numbers such as 3, 4, and 5 are called consecutive integers.
Make and test a conjecture about the sum of any three consecutive integers.
Make and test a conjecture about the sign of the product of any three negative integers.
Counterexample
Example 5
Conjecture: The sum of two numbers is always greater than the larger number.
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Conjecture: The value of x2 is always greater than the value of x.
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Draw real-life examples of points, lines and planes.
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Geometry 2
1.2 Points, Line and Planes
Unit 1: Basics of Geometry
Definition
Undefined
Terms
Building Blocks
of Geometry
Point
Line
Plane
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Activity: Modeling Intersections
McDougall Littell Geometry
Page 12
10
Collinear
Coplanar
Line Segment
Ray
Initial Point
Between
Opposite Rays
11
Draw a sketch illustrate the meaning of the following statements.
The Segment Addition Postulate states that AB + BC = AC if B is between A and C and the
points are collinear.
If the points are not collinear, then AB + BC > AC.
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Geometry 1
1.3 Segments and Their Measures
Postulates
Unit 1: Basics of Geometry
Ruler Postulate
Segment Length
Example 1
Measure the length of the segment to the nearest
millimeter
D
E
Between
Segment
Addition
Postulate
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Use the map to determine the distance from Nico’s to Casa Grande Union High School.
Each grid line represents 1/4th a mile.
What is the distance “as the crow flies?”
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Example 2
Two friends leave their homes and walk in a
straight line toward the others home. When they
meet, one has walked 425 yards and the other has
walked 267 yards. How far apart are their homes?
The Distance
Formula
Example 3
Congruent
Segment
Markings
15
Explain how the distance formula and Pythagorean Theorem are related.
Draw a picture to illustrate your thoughts.
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Distance
Formula and the
Pythagorean
Theorem
B(x2, y2)
|y2 – y1|
A(x1, y1)
C(x2, y1)
|x2 – x1|
c
a
b
Example 4
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Activity: Geometric Constructions
McDougall Littell Geometry
Page 25
18
Mixed review
Page 24 60-71 all
60.
Picture for 68 – 71
61.
68.
Picture for 62-67
69.
62.
70.
63.
71.
64.
65.
66.
67.
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Activity: Paper Folding
McDougall Littell Geometry
Page 31 #54
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Geometry 1
1.4 Angles and Their Measures
Angle
Unit 1: Basics of Geometry
Sides
Vertex
Naming and angle
Example 1
D
A
1
B
C
Protractor
Things to Know
21
22
Measure of an Angle
Congruent Angles
Angle measure
notation
Protractor postulate
A
O
B
Step 1
Step 2
Step 3
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Interior
Exterior
Angle Addition
Postulate
Example 2
The backyard of a house is illuminated by a light fixture that has two bulbs.
Each bulb illuminates an angle of 120°.
If the angle illuminated only by the right bulb is 35°, what is the angle illuminated by
both bulbs?
Acute angle
Right angle
Obtuse angle
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What is wrong with this statement?
Angles that share a common side are adjacent.
Draw a picture of adjacent angles.
Draw a picture of angles that share a side but are not adjacent.
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Straight angle
Example 3
Adjacent angles
Example 4
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Activity: Folding Bisectors
McDougall Littell Geometry
Page 33
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Mixed Review
Page 32 #61-79
61.
65.
62.
66.
63.
67.
64.
68.
Picture for 70-73
69.
70.
72.
71.
73.
74.
75.
76.
77.
78.
79.
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Construction: Segment Bisector and Midpoint
McDougall Littell Geometry
Page 34
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Geometry 1
1.5 Segment and Angle Bisectors
Midpoint
Unit 1: Basics of Geometry
Bisect
Segment bisector
Compass
Straightedge
Construction
Midpoint Formula
Example 1
Example 2
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Construction: Angle Bisector
McDougall Littell Geometry
Page 36
32
Example 3
Example 4
Angle bisector
Example 5
Example 6
Example 7
33
Draw an example of lines adjacent angles that form vertical angles.
Draw an example of adjacent angles that do not form vertical angles.
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Geometry 1
1.6 Angle Pair Relationships
Vertical angles
Unit 1: Basics of Geometry
Linear pair of angles
Example 1
2
1
3
5 4
Example 2
35
What is the difference between supplementary angles and a linear pair of angles? Draw
examples to illustrate your explanation.
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Example 3
M
(4x + 15)°
P (5x + 30)°
N
(3y + 15)° (3y – 15)°
L
O
Complementary
angles
Supplementary
angles
Example 4
Example 5
Example 6
Example 7
37
Use Illustrations to show how the area formulas are related to each other.
How is the area of a rectangle use to find the area of a parallelogram, and triangle?
How is the formula for a parallelogram used to find the area of a circle?
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Geometry 1
1.7 Introduction to Perimeter, Circumference, and Area
Square
Unit 1: Basics of Geometry
Rectangle
Triangle
Circle
Example 1
Find the perimeter and area of a rectangle of length 4.5m and width 0.5m.
Example 2
A road sign consists of a pole with a circular sign on top. The top of the circle is 10 feet
high and the bottom of the circle is 8 feet high.
Find the diameter, radius, circumference and area of the circle. Use π ≈ 3.14.
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Example 3
Find the area and perimeter of the triangle defined by H(-2, 2), J(3, -1), and K(-2, -4).
Example 4
A maintenance worker needs to fertilize a 9-hole golf course. The entire course covers a
rectangular area that is approximately 1800 feet by 2700 feet. Each bag of fertilizer
covers 20,000 square feet. How many bags will the worker need?
Example 5
You are designing a mat for a picture. The picture is 8 inches wide and 10 inches tall.
The mat is to be 2 inches wide. What is the area of the mat?
Example 6
You are making a triangular window. The height of the window is 18 inches and the area
should be 297 square inches. What should the base of the window be?
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