Download Unit 2 - Reasoning in Geometry - KEY

2.1, 2.2, 2.3 Inductive Reasoning, Finding the nth Term, Mathematical Modeling
DISCOVERING GEOMETRY
LEQ:
Guided Notes
Name _________________________________Block_________
How is inductive reasoning used to find the next term in a numerical or geometric sequence?
How is inductive reasoning used to find patterns and apply mathematical models in order to
solve problems?
2.1 Inductive Reasoning
Complete the VOCABULARY chart below. Pages 96-113.
Term
Definition
1. Inductive reasoning
p.96
The process of observing
data, recognizing
patterns, and making
generalizations about
those patterns.
Picture/Symbol
Look carefully at the following figures. Then, use
inductive reasoning to make a conjecture about the
next figure in the pattern
If you have carefully observed the pattern, may be
you came up with the figure below:
2. Conjecture
p. 96
A generalization
resulting from inductive
reasoning.
Consider the example above. The conjecture is that
the pattern repeats clockwise in each corner.
3. Function notation
p. 103
A convention for
expressing a
Function rule in terms of
its input. For example,
f (x) is the output of a
function f whose input is
x.
f(x) = 2x - 3
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4. Mathematical models
p. 108
A mathematical way of
representing a realworld situation, such as
a geometric figure,
graph, table, or
equation.
Complete INVESTIGATION 2.1 “Shape Shifters” on page 98:
Complete EXERCISES on pages 98-101 # ________________, using a separate piece of paper. Use a
proper heading as always.
2.2 Function Notation
Complete the INVESTIGATION 2.2 “Finding the Rule”. See pages 102-103.
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Complete EXERCISES on pages 105-107 # _________________. Use a separate piece of paper.
2.3 Mathematical Modeling
Complete the INVESTIGATION 2.3 “Party Handshakes” below.
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Complete EXERCISES pages 112-113 # ________________.
2.4 Deductive Reasoning
LEQ: How is the deductive reasoning process used to learn the relationship between inductive and
deductive reasoning?
Complete the VOCABULARY below. Begin on page 114-121.
Term
Definition
1. Deductive
Reasoning
p. 114
The process of
showing
that certain
statements follow
logically from
agreed-upon
assumptions and
proven facts.
Picture/Symbol
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2. Network
p.120
A collection of
points connected
by paths.
Complete the INVESTIGATION 2.4 “Overlapping Segments” below.
Complete EXERCISES pages 117-119 # _______________, on a separate piece of paper with proper
heading.
2.5 Angle Relationships
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LEQ: How do you identify and use angle relationships in order to perform investigations and write
conjectures?
No VOCAB for this section.
Complete INVESTIGATION 1 “The Linear Pair Conjecture” below.
Complete INVESTIGATION 2 “Vertical Angles Conjecture” below.
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Complete the EXERCISES on pages 124-127 # _________________, using a separate piece of paper.
2.6 Special Angles on Parallel Lines
LEQ: How are angle relationships explored when parallel lines are cut by a transversal?
Complete the VOCABULARY chart below. See pages 128-131.
Terms
Definition
Picture/Symbol
1. Transversal
p.128
A line that intersects two or more other
coplanar lines.
2. Corresponding
angles
p.128
Two angles formed by a transversal
intersecting two lines that lie in the same
position relative to the two lines and the
transversal.
3. Alternate interior
angles
p.128
A pair of angles, formed by a transversal
intersecting two lines, that lie between the
two lines and are on opposite sides of the
transversal.
4. Alternate exterior
angles
p.128
A pair of angles, formed by a transversal
intersecting two lines, that do not lie
between the two lines and are on opposite
sides of the transversal.
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5. Parallel lines
Lines are parallel if they lie in the same
plane and do not intersect. Line segments or
rays are parallel if they lie on parallel lines.
Complete the INVESTIGATION 1 “Which Angles are Congruent?” below.
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Complete INVESTIGATION 2 “Is the Converse True?” below.
Complete EXERCISES pages 131-134 # _________________ on a separate piece of paper
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Unit 2 Algebra Skills: Slope and Fractals
LEQ:
Why is slope a measure of steepness? How is slope calculated?
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Part 1: Slope
Complete the VOCABULARY chart below. See pages 135-139.
Term
Definition
Picture/Symbol
1. slope
p. 138
In a two-dimensional coordinate system,
the ratio of the vertical change to the
horizontal change between two points on a
line.
2. slope
formula
n/a
3. slope
triangle
p. 135
A right triangle used to find the slope of a
line. The hypotenuse of a slope triangle is
the segment between two points on the
line and its legs are parallel to the
coordinate axes.
4.
recursive
rules
p. 137
A rule that uses the previous term(s) of a
sequence to find the current term
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http://www.narragansett.k12.ri.us/resources/necap%20supp
5. iterate
the act of repeating a process with the aim
of approaching a desired goal, target or
result
6. fractal
p.137
A self-similar geometric figure
7. selfsimilar
p.137
The property that a figure is similar
to part of itself
http://math.rice.edu/~lanius/images/real.gif
http://www2.edc.org/makingmath/mathtools/iteration/mid
8.
is a fractal and attractive fixed set with the
Sierpinski’s overall shape of an equilateral triangle,
Triangle
subdivided recursively into smaller
equilateral triangles
Complete EXERCISES on page 136 # _________________.
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Part 2: Patterns in Fractals.
Complete the ACTIVITY “The Sierpinski Triangle” below.
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