Geometry
Name____________________________________
Chapter 2: Reasoning and Proof
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Day
Topic
Assignment
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1
2.1 Use inductive reasoning. What is a conjecture? What is inductive reasoning? What is a counterexample?
2.1 Workbook.
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2
2.2 Analyze conditional statements. What is a conditional statement? What is a hypothesis? What is a conclusion? How do you
write a conditional statement in “if-then” form? What is the negation of a statement? How do you write the converse of a
conditional statement? How do you write the inverse of a conditional statement? How do you write the contrapositive of a
conditional statement? What are equivalent statements? What is a biconditional statement?
2.2 Workbook.
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3
2.3 Apply deductive reasoning. What is deductive reasoning and how is it different from inductive reasoning? What is the Law of
Detachment? What is the Law of Syllogism?
2.3 Symbolic notation. Let p be “the angle is a right angle” and let q be “the measure of the angle is 90ᵒ.”
Conditional. If p, then q. 𝑝 → 𝑞. If an angle is a right angle, then its measure is 90ᵒ.
Converse. If q, then p. 𝑞 → 𝑝. If the measure of an angle is 90ᵒ, then the angle is a right angle.
Inverse.
If not p, then not q. ~𝑝 → ~𝑞. If an angle is not a right angle, then its measure is not 90ᵒ.
Contrapositive. If not q, then not p. ~𝑞 → ~𝑝. If the measure of an angle is not 90ᵒ, then the angle is not a right angle.
Biconditional. p if and only if q. 𝑝 ↔ 𝑞. An angle is a right angle if and only if its measure is 90ᵒ.
2.3 Workbook
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Book page 95
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4
2.4 Use postulate and diagrams.
a) Through any two points there exits exactly one line.
b) A line contains at least two points.
c) If two lines intersect, then their intersection is exactly one point.
d) Through any three noncollinear points there exists exactly one plane.
e) A plane contains at least three noncollinear points.
f) If two points lie in a plane, then the line containing them lies in the plane.
g) If two planes intersect, then their intersection is a line.
h) A line perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every point in
the plane that intersects it at that point.
2.4 Workbook.
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5
2.5 Reasoning using properties from Algebra. What are properties of equality?
Reflexive property of equality: a = a. This is true for sides and angles.
Symmetric property of equality: if a = b, then b = a. This is true for sides and angles.
Transitive property of equality: if a = b and b = c, then a = c. This is true for sides and angles.
Distributive property: 𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐.
2.5 Workbook.
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2.6 Prove statements about segments ad angles. What is a proof? What is a two-column proof?
2.6 Workbook.
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2.7 Prove angle pair relationships.
a) Right angles congruent theorem. All right angles are congruent.
b) Congruent supplement theorem. If two angles are supplementary to the same angle (or to congruent angles), then they
are congruent. If < 1 and < 2 are supplementary and < 3 and < 2 are supplementary, then < 1 ≅ < 3.
c) Congruent complement theorem. If two angles are complementary to the same angle (or to congruent angles), then they
are congruent. If < 1 and < 2 are complementary and < 3 and < 2 are complementary, then < 1 ≅ < 3.
d) Linear pair. If two angles form a linear pair, then they are supplementary.
e) Vertical angle congruence theorem. Vertical angles are congruent.
2.7 Workbook.
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Chapter 2 review.
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Chapter 2 Exam. You have one shot at it so give it your very best effort.
pp. 134-137
1-24 all
Total points
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I still have questions about:
Homework Rubric
Score: 0
I didn’t do the assignment.
Score: 1
Score: 2
Score: 3
Score: 4
I did at least 50% of the assignment. I
did the assignment by the end of the
chapter.
I did at least 75% of the assignment. I
did the assignment by the end of the
chapter.
I did 100% of the assignment. I did the
assignment on time.
I did 100% of the assignment. I did the
assignment on time.
I showed some work.
I showed most of my work.
I showed all my work.
I showed all my work.
I checked some of my answers with
similar problems in the textbook or
online book.
I checked most of my answers with
similar problems in the textbook or
online book.
I checked all my answers with similar
problems in the textbook or online book.
I checked all my answers with similar
problems in the textbook or online book.
If I had questions, I didn’t seek help.
If I had questions, I sought help most of
the time.
If I had questions, I sought help all the
time.
If I had questions, I sought help all the
time. I taught the material to a
classmate, friend, or adult.
Where can I get help?
My classmates. Form a study group! Get phone numbers or emails of classmates.
My parents or other adults. They are smarter than you think! Besides, it creates good bonding time.
My teacher. I’m in the Math Department Office (E200) from 7:00-7:30am and 1:50-2:30 every day. I
also have 3rd period planning so you can get help from me. I have advisory in F203 and you are
encouraged to come and get help from me during travel days.
Textbook and its tutorial website, www.classzone.com. Select Little: Geometry 2007, then choose code
(ask me). Go to the online book at the bottom of the screen and choose the desired chapter. There are lots
of practice problems here.
Free Tutoring. Let me know if you need a tutor.
The World Wide Web. Check out the documents and links at
http://teacher.edmonds.wednet.edu/edmondswoodway/swahbeh