Foundations of Math II Unit 3: Similarity and Congruence .Unit 3: Similarity and Congruence ... Record

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  • Foundations of Math II

    Unit 3: Similarity and

    Congruence

    Academics

    High School Mathematics

  • 1

    3.1 Warm Up

    1. Jill and Bill are doing some exercises. Jayne Funda, their instructor, gently implores Touch

    your nose to your knees, maggots! Their attempts to please Ms. Funda are shown below.

    Bills says, Im doing better than you, Jill. My nose is much closer to my knees!

    Jill replies, That isnt a fair comparison, Bill.

    With whom do you agree? Who is doing a better job? Explain your answer.

    2. The perimeter of COW is 12 units.

    a) Find possible lengths for , , and .

    b) Find four more sets of possible lengths.

    c) How many answers are possible?

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii

    Jill Bill

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    3.2 Warm Up

    1. Which of the figures below could be the image of figure a when dilated? Explain why or why

    not for each figure.

    2) a) Draw a line that passes through the origin of a coordinate plane and

    forms a 45 angle with the x-axis.

    b) Find the coordinates of at least three points on the line.

    c) Write an equation for the line. What do you notice?

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii

    a

    s

    g

    r

    p

    e

    f

    c

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    3.2 Practice with Dilations on the Coordinate Plane

    Graph three points that lie in three different quadrants and connect them to form a triangle. Label

    the vertices of the triangle as TRI.

    Record the coordinates of the triangle in the table below. Then find and apply the algebraic rules

    for each of the scale factors listed below. Graph and label each image.

    Scale Factor

    2

    Algebraic Rule (x, y) (x, y) (x, y)

    T ( , ) T ( , ) T ( , ) T ( , )

    R ( , ) R ( , ) R ( , ) R ( , )

    I ( , ) I ( , ) I ( , ) I ( , )

    What would each scale factor be if written as a percent?

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    Explain why or why not for each pair.

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    Find the scale factor. The pre-image is indicated by an arrow.

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    3.3 Warm Up

    1. Draw each of the following dilations of quadrilateral BRIA:

    a. 150% scale factor using center X.

    b. 3

    2 scale factor using center Y.

    c. 1.5 scale factor using center I.

    d. What do you notice?

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii

    Y

    A

    I

    B

    R

    X

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    3.4 Warm Up

    1) a) If a line has a slope greater than 1, what angle might it make with the x-axis?

    b) If a line has a slope less than 1, what angle might it make with the x-axis?

    c) If a line has a slope equal to 1, what angle might it make with the x-axis?

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii

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    3.4 Midsegment Example Problems

    Example 1

    Find x.

    Example 2

    DE is the midsegment of ABC. Find x, AC, and ED.

    Example 3

    MN is the midsegment of JKL.

    MN = 2x + 1

    KJ = 5x 8

    Find x, MN, and KJ.

    Example 4

    28 7x

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    3.4 Midsegments Show What You Know!

    1) XY is the midsegment of RST. Find each requested measure based on the given information.

    a) XY = 16, RS = ?

    b) RS = 22, XY = ?

    c) XY = 5x, RS = 15, x = ?

    d) mR = 23, mTXY = ?

    e) mXYS = 137, mYSR

    2) Find x and y.

    3) Find MS, PT, and ST.

    4)

    a)

    b)

    c)

    3y

    18

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    3.5 Warm Up

    1) a) A line forms an angle measuring less than 45 with the x-axis. What might its slope

    be?

    b) A line forms an angle measuring more than 45, but less than 90, with the x-axis.

    What might its slope be?

    c) What might the slope be if the line forms an obtuse angle with the x-axis?

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii

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    3.6 Warm Up

    1) A line passes through the origin and the point A(7, 3). Without graphing the line, what

    can you conclude about the angle it will form with the x-axis?

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii

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    3.7 Warm-up

    1. Erica builds a ramp that makes a 45 with the ground. Her support board is 10 feet from the

    beginning of the ramp.

    a. How high is her support board?

    b. How long is her ramp?

    2. Line m forms a 40 angle with the x-axis. Find the slope of line m. Explain your answer?

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group,

    College of Education at the University of Hawaii.

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    3.8 Warm Up

    1) Bill builds a ramp at a 56 angle with the ground. He uses a 12-foot support board and finds

    that the support board must be 8 feet from the beginning of the ramp in order to make the 56

    angle. Jill also builds a ramp at a 56 angle with the ground. She uses a 9-foot support board.

    How far should her board be from the beginning of her ramp? Illustrate and explain your

    answer.

    Adapted from Geometry: A Moving Experience developed by the Curriculum Research & Development Group, College of Education at the University of Hawaii

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    Vocabulary Word

    Definition Characteristics Picture and/or

    Symbol Real Life Examples

    AAS

    ASA

    congruent

    dilation

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    Vocabulary Word

    Definition Characteristics Picture and/or

    Symbol Real Life Examples

    extremes

    flow proof

    geometric mean

    means

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    Vocabulary Word

    Definition Characteristics Picture and/or

    Symbol Real Life Examples

    midsegment

    Midsegment Theorem

    proof

    proportion

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    Vocabulary Word

    Definition Characteristics Picture and/or

    Symbol Real Life Examples

    SAS

    scale factor

    side

    similar

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    Vocabulary Word

    Definition Characteristics Picture and/or

    Symbol Real Life Examples

    SSS

    triangle

    Triangle Angle Sum Theorem

    vertex

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    Vocabulary Word

    Definition Characteristics Picture and/or

    Symbol Real Life Examples

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