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Transcript
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: