Reasoning and Proofs

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Chapter 2-4 2-5

• Reasoning and Proofs

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Lesson 5 MI/Vocab

• postulate

• Identify and use basic postulates about points,
  lines, and planes.

• axiom
• theorem
• proof
• paragraph proof
• informal proof

• Write paragraph proofs.

Standard 1.0 Students demonstrate understanding
by identifying and giving examples of undefined
terms, axioms, theorems, and inductive and
deductive reasoning. (Key) Standard 2.0 Students
write geometric proofs, including proofs by
contradiction. (Key) Standard 3.0 Students
construct and judge the validity of a logical
argument and give counterexamples to disprove a
statement. (Key)
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Lesson 4 Ex1
Determine Valid Conclusions
A. The following is a true conditional.
Determine whether the conclusion is valid based
on the given information. Explain your reasoning.
If two segments are congruent and the second
segment is congruent to a third segment, then the
first segment is also congruent to the third
segment.
Answer Since the conditional is true and the
hypothesis is true, the conclusion is valid.
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Lesson 4 Ex1
Determine Valid Conclusions
B. The following is a true conditional.
Determine whether the conclusion is valid based
on the given information. Explain your reasoning.
If two segments are congruent and the second
segment is congruent to a third segment, then the
first segment is also congruent to the third
segment.
Answer According to the hypothesis for the
conditional, you must have two pairs of congruent
segments. The given only has one pair of
congruent segments. Therefore, the conclusion is
not valid.
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Lesson 4 CYP1
A. The following is a true conditional. Determine
whether each conclusion is valid based on the
given information. Explain your reasoning. If a
polygon is a convex quadrilateral, then the sum
of the interior angles is 360.Given m?X m?N
m?O 360Conclusion If you connect X, N, and
O with segments, the figure will be a convex
quadrilateral.

1. A.
2. B.
3. C.

A. valid B. not valid C. cannot be determined
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Lesson 4 CYP1
B. The following is a true conditional. Determine
whether each conclusion is valid based on the
given information. Explain your reasoning. If a
polygon is a convex quadrilateral, then the sum
of the interior angles is 360.Given ABCD is a
convex quadrilateral.Conclusion The sum of the
interior angles of ABCD is 360.

1. A.
2. B.
3. C.

A. valid B. not valid C. cannot be determined
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Lesson 4 KC2

• Law of Syllogism (the name is not important)
• If you do your homework, then you will do well on
  the tests.
• If you do well on the tests, then you will pass
  the class.
• Conclusion
• If you do your homework, then you will pass the
  class.

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Lesson 4 Ex2
Determine Valid Conclusions From Two Conditionals
A. PROM Use the Law of Syllogism to determine
whether a valid conclusion can be reached from
each set of statements. (1) If Salline attends
the prom, she will go with Mark.(2) If Salline
goes with Mark, Donna will go with Albert.
Answer If Salline attends the prom, Donna will
go with Albert.
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Lesson 4 Ex2
Determine Valid Conclusions From Two Conditionals
B. PROM Use the Law of Syllogism to determine
whether a valid conclusion can be reached from
each set of statements. (1) If Mel and his date
eat at the Peddler Steakhouse before going to
the prom, they will miss the senior march.
(2) The Peddler Steakhouse stays open until 10
P.M.
Answer There is no valid conclusion. While both
statements may be true, the conclusion of each
statement is not used as the hypothesis of the
other.
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Lesson 4 CYP2
A. Use the Law of Syllogism to determine whether
a valid conclusion can be reached from each set
of statements.(1) If you ride a bus, then you
attend school.(2) If you ride a bus, then you
go to work.
A. valid B. not valid C. cannot be determined

1. A.
2. B.
3. C.

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Lesson 4 CYP2
B. Use the Law of Syllogism to determine whether
a valid conclusion can be reached from each set
of statements.(1) If your alarm clock goes off
in the morning, then you will get out of bed.
(2) If you ride a bus, then you go to work.
A. valid B. not valid C. cannot be determined

1. A.
2. B.
3. C.

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Lesson 5 PS1
Attention You do not have to write down or
memorize these postulates. You will need to refer
to them on tonights assignment. They are on page
105 in the book.
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Lesson 5 Ex1
Points and Lines
SNOW CRYSTALS Some snow crystals are shaped like
regular hexagons. How many lines must be drawn to
interconnect all vertices of a hexagonal snow
crystal?
Explore The snow crystal has six vertices since a
regular hexagon has six vertices. Plan Draw a
diagram of a hexagon to illustrate the solution.
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Lesson 5 Ex1
Points and Lines
Solve Label the vertices of the hexagon A, B, C,
D, E, and F. Connect each point with every other
point. Then, count the number of segments.
Between every two points there is exactly one
segment. Be sure to include the sides of the
hexagon. For the six points, fifteen segments
can be drawn.
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Lesson 5 Ex1
Points and Lines
Answer 15
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Lesson 5 CYP1
ART Jodi is making a string art design. She has
positioned ten nails, similar to the vertices of
a decagon, onto a board. How many strings will
she need to interconnect all vertices of the
design?
A. 20 B. 70 C. 35 D. 45

1. A
2. B
3. C
4. D

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Lesson 5 PS2
Attention You do not have to write down or
memorize these postulates. You will need to refer
to them on tonights assignment. They are on page
106 in the book.
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Lesson 5 Ex2
Use Postulates
Answer Always Postulate 2.5 states that if two
points lie in a plane, then the entire line
containing those points lies in the plane.
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Lesson 5 Ex2
Use Postulates
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Lesson 5 Ex2
Use Postulates
C. Determine whether the following statement is
always, sometimes, or never true. Explain.
Answer Never noncollinear points do not lie on
the same line by definition.
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Lesson 5 CYP2
A. Determine whether each statement is always,
sometimes, or never true. Explain. Plane A and
plane B intersect in exactly one point.
A. always B. sometimes C. never

1. A.
2. B.
3. C.

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Lesson 5 CYP2
B. Determine whether each statement is always,
sometimes, or never true. Explain. Point N lies
in plane X and point R lies in plane Z. You can
draw only one line that contains both points N
and R.
A. always B. sometimes C. never

1. A.
2. B.
3. C.

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Lesson 5 CYP2
C. Determine whether each statement is always,
sometimes, or never true. Explain. Two planes
will always intersect to form a line.
A. always B. sometimes C. never

1. A.
2. B.
3. C.

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Lesson 5 KC1
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Lesson 5 TH1
Midpoint Theorem
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Homework

• Pg 102
• 9 20 and
• Pg 108
• 8 20, 32 35