Download CH 1 Math Notes

Chapter 1 Math Notes
#1 Symmetry
Three Kinds of Symmetry:
1. __________ Symmetry: When it is possible to draw a ___________ _______
that _______ the figure back onto itself.
Do these have Reflection Symmetry?
Ex 1.
Ex 2.
2. ___________ Symmetry: When it is possible to ______ the figure so it maps
onto itself.
Do these have Rotation Symmetry?
3. ____________ Symmetry: When it is possible to _____ the figure so it maps
onto itself.
No __________ have translation symmetry, but what about this line?
Try these. What symmetries do they have?
#2 Slope Formula and Distance Formula
Using points (-2, 4) and (3, 5). Draw the Graph:
Slope Formula:
Distance Formula:
Find the Slope:
Find the Distance:
#3 Proportions
In a proportion like
𝑎
𝑏
=
𝑐
𝑑
, when you _________the corners they will be ______.
So _______ = ________. We can solve the equation from here.
Ex 1.
Ex 3.
𝑥
3
=
10
2𝑥−1
4
Ex 2.
15
=
14
8
1
8
Try This!
=
𝑥
12
10
2𝑥+2
=
25
20
#4 Geometry Vocab
TERM—DEFINITION--PICTURE
Point: An exact ________ or _________
Named using a _________ ___________ letter.
Line: Extends infinitely in _____ directions.
Line Segment: A portion of the line between two __________.
Vertex: The _______ where two ______ meet to form a “corner”.
Geometry Vocab Continued
Plural of vertex is ___________.
Ray: Part of a line that starts at a _________ and extends infinitely in _____
direction.
Angle: Formed by two _____ joined at their ______.
Measure of Angle: How _____ and angle is. Measured in __________.
Draw Pictures:
Scalene Triangle: _______ sides are the same length.
Isosceles Triangle: _______ sides are the same length.
Equilateral Triangle:
_______ sides are the same length.
#5 Linear Models
Linear Functions model situations that grow by _______ __________ over equal
intervals. Linear Functions are increasing or decreasing at a __________ rate.
Remember that the equation of a linear function can be written in the form:
Y = mx + b. m  ________ and b  _____________.
Ex. 1: Draw the graph of y = 2x – 3.
M = _______
B = _______
What is the x-intercept of this line?
Ex. 2: Allison opens a savings account by depositing $500. She plans to add $125
to the account per month. Write a linear function to express this.
Ex. 3: Write the linear equation of the line that goes through (3,7) and (9,9).
Ex. 4: Write the linear equation of the line that goes through (-1, 4) and (5, -2).
#6 Area Model Products and Sums
The area of a rectangle can be written two different ways:
1. _________ of Length x Width
2. _________ of all the individual areas.
Ex 1. The area of this rectangle can be written two different ways.
An _____ _________ enables us to represent the same thing without using the
algebra tiles.
Ex 2. Write the area of this rectangle as a product and as a sum.
Now draw an area model.
Area Model Products and Sums continued..
Ex 3. Write the area of this rectangle as a product and as a sum.
Now draw an area model.
#7 Exponential Functions
Remember that exponential functions are in the form y = abx, where
a = initial value
b = factor or multiplier
Exponential Functions Continued…
#8 Transformations
Ex 1: Graph Triangle ABC where:
A: (-2, 3)
B: (-5, 3)
C: (-5, 7)
Transformation #1:
Reflect the triangle over the x-axis.
Transformation #2:
Rotate
A’B’C’ 90 degrees counterclockwise.
Transformation #3:
Translate
A’’B’’C’’ 5 up and 2 right.
Ex 2: Graph Triangle PQR where:
P: (3, 1)
Q: (3, 6)
R: (1, 6)
Transformation #1:
Reflect the triangle over the y-axis.
Transformation #2:
Rotate
P’Q’R’ 180 degrees counterclockwise.
Transformation #3:
Translate
P’’Q’’R’’ 2 down and 5 left.
#9 Angle Pair Relationships
Complementary Angles: two angles whose measures ______________________.
Examples:
Supplementary Angles: two angles whose measures ______________________.
Examples:
A ______________ is a line that cuts across any two other lines.
________________: a pair of opposite angles formed by two intersecting lines.
Example:
Vertical Angles Theorem: if angles are vertical then they are ____________.
If two parallel lines are cut by a transversal, then the following relationships are
true:
Corresponding Angles are _______.
Ex:
Alternate Interior Angles are ________
Ex:
Same-side Interior Angles are __________
Ex:
Alternate Exterior Angles are __________
Ex:
Same-Side Exterior Angles are __________
Ex: