Lesson 2.4 - Reasoning in Algebra

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Lesson 2.4 - Reasoning in Algebra Lesson 2.5 -
Proving Angles Congruent
The other day I was driving down the road and
saw a banana peeland swerved. Thank you Mario
Kart.
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Deductive Reasoning - Justifying Your Steps
Proof is a way of thinking. In math, we have
processes that we go through every time we solve
a problem. All proof does is help us use
deductive reasoning to break down our thinking
and justify each step we take.
1 minute in groups Discuss two pros about proofs,
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Justifying Steps
Example Solve for x and justify each step.
B
A
x?
Given
(2x10)?
C
O
Statement
Reason
x 2x 10 139
3x 10 139
3x 129
x 43
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Justifying Steps
Example Solve for m and justify each step
Given XZ 32
Reason
Statement
XZ 32
XY YZ XZ
2m 5m 11 32
7m 11 32
7m 21
m 3
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Terms/Properties
Theorem a statement that is proven
Review so we can use them
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Vertical Angles Theorem
Theorem 2.1 Vertical angles are congruent
Prove it!
Given and are vertical angles Prove
Statement
Reason
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Use It!
Find the value of x.
(7x 6)o
(2x 9)o
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Congruent Supplements Theorem
Theorem 2.2 If two angles are supplements to the
same angle (or congruent angles), then the two
angles are congruent
is supplementary to
is supplementary to
What can we conclude?
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Congruent Complements Theorem
Theorem 2.3 If two angles are complements of the
same angle then they are congruent Ex lt1 is
complementary to lt2 AND lt3 is complementary to
lt2 SO lt1 is congruent to lt3 Theorem 2.4
All right angles are congruent Theorem 2.5 If
two angles are congruent and supplementary, then
each is a right angle
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Lesson 2.4 - Reasoning in Algebra Lesson 2.5 -
Proving Angles Congruent
HW 1. Pgs. 105-108 2-22 e, 28, 44-49 all 2.
Pgs. 112-115 1-3 all, 7-18 all, 21, Challenge
30, 32 Both Due Tues. (10/5)Tools Vertical
Angles Theorem, Congruent Supplements Theorem,
Congruent Complements Theorem
The other day I was driving down the road and
saw a banana peeland swerved. Thank you Mario
Kart. -Jodi Strathman