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Transcript
Unit 1 PACKET (1.2-1.8 (Omit 1.6), 2.6, 3.1-3.4)
DATE
LESSON
ESSENTIA
L
QUESTIO
N
I WILL….
Assignments (Day
1)
BW:
 Vocab and
8/22
Due:
8/25 or
8/26
Lesson 1.2:
Points,
Lines, and
Planes
Pages 11-19
What are the
accepted
facts and
basic terms
and
definitions of
geometry?
Postulate Chart
CW/HW:
Use the textbook to
 Lesson 1.2
define, name, and draw
Notes
the accepted facts and
basic terms of
 Pg.16 #1-3
geometry.
 WB 9
EXIT:
1. Pg.16 #5
and #7
BW:
8/23
Due:
8/25 or
8/26
Lesson 1.3:
Measuring
Segments
Pages 20-26
How can you
use number
operations to
find and
compare
lengths of
segments?
Use number operations
to find and compare
lengths of segments.

#1
CW/HW:

Vocab

Lesson 1.3
Notes

Pg.23 #1-6

WB 13
EXIT:

Page 24 #7
BW:
8/24
Lesson 1.4:
Measuring
Angles
Due:
8/25 or
8/26
Pages 27-33
How can you
use number
operations to
find and
compare the
measure of
angles?

Use number operations
to find and compare the
measure of angles.
Key concepts
/Postulate 1.8
CW/HW:
 Lesson 1.4
Notes
 Pg.31 #1-4
 WB17
EXIT:
 Pg.31 #5
BW:

8/25
Or
8/26
Due:
8/25 or
8/26
Lesson 1.5:
Exploring
Angle Pairs
Pages 34-40
How can
special angle
pairs help
you identify
geometric
relationships?

Use special
angle pairs to
find angle
measures.
#2
CW/HW:
 KC/V/P1.9
 Lesson 1.5
Notes
 Pg.37 #1-5
 WB 19-20
#4-7, 9, 17,
20
 WB 21
EXIT: pg.37 #6
Assignments
(Day 2)
8/29
8/30
Due:
9/1
Or
9/2
8/31
9/1(2)
Due:
9/1
Or
9/2
9/1(2)
Due:
9/6
9/7
9/8(9)
Due:
9/8(9)
Lesson 1.7:
Midpoint
and
Distance in
the
Coordinate
Plane
How can you
find the
midpoint and
length of any
segment in a
coordinate
plane?
Use the midpoint and
distance formulas to
find the length of
segments in the
coordinate plane.
Pages 50-56
Lesson 1.8:
Perimeter,
Circumferen
ce, and Area
Pages 59-67
How do you
find the
perimeter and
area of
geometric
figures?
Use the formulas for
perimeter and area
measure geometric
figures.
BW:
 #3
CW/HW:
 KC
 Lesson Notes
1.7
 Pg.53 #1-4
EXIT:
 Pg.53 #5
 Pg.55 #5253
BW:
 #4
CW/HW:
 KC/V/P1.10
 Lesson Notes
1.8
 Pg.64 #1-3
EXIT:
Pg.64 #6
Due:
9/15
(16)
9/14
9/15(6)
Due:
9/15
(16)
EXIT:

Pg.55 #56
BW:
 Pg.65 #27, 32
CW/HW:
 WB 31-32
(even)
 WB 33
EXIT:
Pg.66 #48
BW:
 Pg.70 #1-4
CW/HW:
 Pg.71-74 #7-41
(odd)
Review/Ass
ess
EXIT:
 Pg.75 #2023
Lesson 2.6:
Proving
Angles
Congruent
How can you
prove
theorems as
reasons in a
proof?
BW:
 Theorems
CW/HW:
Prove and apply
 Lesson Notes
12.6
theorems about angles.
 Pg.124 #1-3, 5
EXIT:

9/12
9/13
BW:
 Pg.54 #31,32
CW/HW:
 WB 27-28
(even)
 WB 29
What
special
Lesson 3.1: angle pairs
Lines and are formed
Angles
by
transversals
?
Lesson 3.2:
Properties
of Parallel
Lines
What are
the
properties of
parallel
lines?
BW:
 #5
CW/HW:
 WB 55-57
EXIT:
Pg.125 #19
Pg.124 #4
BW:
BW:
 KC
 #6
CW/HW:
Identify the special
CW/HW:
 Lesson 3.1
angle pairs formed by
 WB 59-61
Notes
EXIT:
a transversal.
 Pg.143 #1-9
 Pg.144
EXIT:
#24
 Pg.143 #10
BW:
Identify and justify
 #7
congruent and
CW/HW:
supplementary angles
 KC
using my knowledge
 Lesson 3.2
of the properties of
Notes
parallel lines.
 Pg.152 #1-5
BW:

Pg.153
#15, 16
CW/HW:
 WB 63-65
EXIT:
EXIT:
 Pg.152 #6
9/15
(16)
BW:
 Pg.132 #38
CW/HW:
 Pg.134 #3237
 Pg.208 #1624
EXIT:
 Pg.211 #17,
18
Review/Ass
essment
9/19
BELL WORK
#1.
#2.

Pg.154
#22
Assessment
Packet 1 Turn in
#3.
#4.
#5.
#6.
#7.
BELL WORK
1.2 Points, Lines, and Planes
Vocabulary Term Description
A _______________ indicates a location
and has no size.
How to Name It
You can represent a point by a _________
and name it with a _________________
___________________.
A ________ is represented by a straight
You can name a line by any _______
path that extends in two ____________
_____________ on the line, or by a single
directions without end and has no
____________ ______ letter.
____________. A line contains infinitely
many ___________.
A ___________ is represented by a
________ surface that extends without
You can name a plane by a
_______ and has no
_____________ letter or by any three
___________________.
__________ in the plane.
A plane contains infinitely many
____________.
What are the names of three collinear
Points that lie on the same _________ are
points?
called _______________ ____________.
Points ____, _____, and ____ are
collinear.
Points and lines that lie in the
What are the names of four coplanar
_____________ plane are
points?
________________. _____ the points of a
Points _____, ____, _____, and ____ are
_______ are coplanar.
coplanar.
_________ is the set of all ____________
in three dimensions.
A ________________ is part of a line that
You can name a segment by its ________
consists of two _____________ and all
__________________.
points _______________ them.
A ______ is part of a line that consists of
the endpoint.
You can name a ray by its _____________
and another ___________ on the ray. The
____________ of the points indicates the
ray’s _________________.
____________ __________ are ________
You can name opposite rays by their
rays that share the ________ endpoint and
__________ endpoint and _______ other
form a _________.
____________ on each ray.
one ________________ and all the
______________ of the line on one side of
Diagram
A __________________ OR
(Please see the table of Postulates
_________________ is an accepted
1-1, 1-2, 1-3, and 1-4 below.)
statement or fact. Postulates, like
________________ terms, are basic
building blocks of the
__________________ system of
geometry. You will use
________________
_____________________ to prove general
concepts.
When you have two or more geometric
figures, their __________________ is the
set of points the ______________ have in
_______________.
Postulate Name
Postulate 1-1
Postulate 1-2
Postulate 1-3
Postulate 1-4
Description
Through any two points there is exactly one __________.
If two distinct lines intersect, then they intersect in exactly
one _______.
If two distinct planes ____________, then they
______________ in exactly one line.
Through any three noncollinear points there is exactly one
_____________.
Diagram
1.3 Measuring Segments
Vocab: The real number that _____________________ to a point is called the ____________________ of the
point. The _________________________ between points A and B is the ____________________
_________________ of the difference of their coordinates, or ______________.
Example 1: Measuring Segment Length
What are UV and SV on the number line above?
UV=
SV=
Postulate 1-6: Segment Addition Postulate
If three points A, B, and C are
___________________ and B is
___________________ A and C,
then AB + BC = AC.
Example 2: Using the Segment Addition Postulate
Example 3: Comparing Segment Lengths
Use the diagram above. Is segment AB congruent to segment DE?
Example 4: Using the Midpoint
1.4 Measuring Angles
Key Concept:
The ___________________ of an angle is the region containing
________________________________________________________________.
The ___________________ of an angle is the region containing
________________________________________________________________.
Example 1: Naming Angles
Key Concept: TYPES OF ANGLES:
Acute angle
Right angle
Between _____ and ______ degrees
Exactly _______ degrees
Obtuse angle
Straight angle
Between ________ and _______ degree
Exactly _______ degrees
Example 2: Measuring and Classifying Angles
What are the measures of angles LKH,
HKN, and MKH?
Classify each angle as acute, right, obtuse, or
straight.
Congruent Angles:
Postulate 1-8 Angle Addition Postulate:
If point B is in the __________________________ of
____________________,
then __________________________________________________.
Example 3: Using the Angle Addition Postulate
1.5 Exploring Angle Pairs
Key Concept: Types of Angle Pairs
Adjacent angles are two coplanar angles
with a common ____________, a common
_____________, and ________ common
interior points.
Vertical angles are two angles whose sides
are _________________________
_________________.
Complementary angles are two angles
whose
____________________________________
___________
___________________________________.
Each angle is called the complement of the
other.
Supplementary angles are two angles whose
____________________________________
___________
___________________________________.
Each angle is called the supplement of the
other.
Example 1: Identifying Angle Pairs
1. 5 and 4 are _________________ angles.
2. 6 and 5 are _________________ angles.
Linear pair:
Linear Pair:
3. 1 and 2 are a _____________________.
Postulate 1-9 Linear Pair Postulate: If two angles for a linear pair, then they are ______________________.
Vocab:
Linear Pair:
Angle bisector:
Example 2: Missing Angle Measures
Angles KPL and JPL are a linear pair. What
are their measures?
Example 3: Using an Angle Bisector to Find Angle Measures
In the diagram,
bisects WXZ.
a. Solve for x and find mWXY.
b. Find mYXZ.
c. Find mWXZ.
1.7 Midpoint and Distance in the Coordinate Plane
Key concept: Formulas:
Midpoint on a number line
Midpoint on a graph
Distance
Example 1: Finding the Midpoint
1. Find the coordinate of the midpoint of the segment with the given endpoints: -8 and 12
2. Find the coordinates of the midpoint of CD.
Example 2: Finding the Endpoint
The coordinates of point S are (9, -3). The midpoint of RS is (6, 10). Find the coordinates of point R.
Example 3: Finding Distance
Find the distance between the pair of points. If necessary, round to the nearest tenth.
C(2, 6), D(10, 8)
1.8 Perimeter, Circumference, and Area
Vocab:
Perimeter, P: ________ of lengths of all __________
Circumference, C: Perimeter of a _______________
Area, A: number of __________ __________it encloses
Key Concept: Formulas
Triangle
Square
Side length s
P=
Side lengths a, b, and c
s
Base b, and height h
P=
c
a
h
A=
A=
b
Rectangle
Base b and
Circle
h
Radius r and diameter d
height h
C=
P=
b
A=
C=
A=
C
You can name a circle with the symbol _________.
Pi = ______ = ________ = ________
Postulate 1-10: Area Addition Postulate: The area of a region is the ________ _____ _____ ________ of its
nonoverlapping parts.
Example #1: Perimeter of a Rectangle
You want to frame a picture that is 5 in. by 7 in. with a 1in.-wide frame.
Example #2: Circumference
a) What is the circumference of a circle with radius of 24
m in terms of π?
C=2πr
C=2π(
C=
)
a) What is the
perimeter of the
picture?
P = 2b + 2h
P=2( )+2(
P=
)
b) What is the perimeter of the outside edge of the frame?
P = 2b + 2h
P=2( )+2(
P =
)
b) What is the circumference of a circle with diameter 24
m to the nearest tenth?
C=πd
C=π(
C=
)
Example #3: Perimeter in the Coordinate Plane
Example #4: Area of a Rectangle
Graph quadrilateral JKLM with vertices J(-3, -3), K(1, -3),
L(1, 4), and M(-3, 1). What is the perimeter of JKLM?
You are designing a poster that will be 3 yd. wide and 8 ft.
high. How much paper do you need to make the poster?
Give your answer in square feet.
P=J+K+L+M
P=
1 yard = ____ feet, so 3 yd. = ______ feet
A = bh
A=( )(
A=
)
Example #5: Area of a Circle
The diameter of a circle is 14 ft.
a) What is the area of the circle in terms of π?
d = 14 feet, so r = ________ feet
Example #6: Area of an Irregular Shape
What is the area of the figure below?
A = π 𝑟2
A = π ( )2
A=π( )
A=
b) What is the area of the circle using an approximation of
π?
2.6 Proving Angles Congruent
Theorem 2-1 Vertical Angles Theorem
Theorem 2-2 Congruent Supplements Theorem
If…
Theorem
If two angles are supplements of
the same angle (or of congruent
angles), then the two angles are
congruent.
Then…
Theorem 2-3 Congruent Complements Theorem
Theorem
If…
Then…
If…
Then…
If…
Then…
If two angles are complements of
the same angle (or of congruent
angles), then the two angles are
congruent.
Theorem 2-4
Theorem
All right angles are congruent.
Theorem 2-5
Theorem
If two angles are congruent and
supplementary, then each is a right
angle.
3.1 Lines and Angles
Key Concept Parallel and Skew
Definition
Parallel lines are
________________ lines that
do not __________________.
The symbol ______ means
“________________________.
”
Skew lines are
___________________; they
are not ___________________
and do not
____________________.
Symbols
Diagram
Parallel planes are planes that
do not ____________________.
Transversal:
Key Concept
Alternate interior angles:
Same-side interior angles:
Alternate exterior angles:
Corresponding angles:
3.2 Properties of Parallel Lines
Same-Side Interior Angles are _____________________________
Alternate Interior Angles are ______________________________
Corresponding Angles are _________________________________
Alternate Exterior Angles are ______________________________
EXITS
EXITS