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BIG IDEA: Reasoning and Proof
ESSENTIAL UNDERSTANDING

Given information, definitions, properties, postulates, and previously proven theorems can be used as reasons in a proof.
MATHEMATICAL PRACTICE
Construct viable arguments and critique the reasoning of others.


Definition: a ____________________ of the meaning of a word or phrase.

Theorem: a ____________________ that is proven

Postulate (or Axiom): an ____________________ statement of fact
Theorems


Given:
EF

GH

Prove: EG

FH
Statements
1.
2. FG

FG
3.
4.
EG

EF

FG
FH

GH

FG
5.
6.
EX 1
Reasons
1. Given
2.
3. Addition Property
4.
5. Substitution Property
6.



Given: AD

8, BC

8, BC

CD
Prove: AD

CD
4.
5.
2.
3.
Statements
1. AD

8, BC

8
AD

BC
Reasons
1.
2. Transitive Property
3.
4. Given
5.
EX 2


Given:
X is the midpoint of MN and MX

RX

Prove:
XN

RX
Statements
1.
2.
3.
4.
MX

XN
XN

RX
EX 3
1. Given
2.
3. Given
4.
Reasons


Given:

Find:
AC

91 x
Statements
4.
5.
6.
7.
1.
2.
3. AB x 10
BC

4 x

1 x

10

4 x
 
5 x

100
EX 4
Reasons
1. Given
2. Segment Addition Postulate
3.
4.
5. Combine like terms
6.
7. Division Property

2.5 p. 105
8, 10, 16 – 18 all, 21, 22 – 34 evens,
37 – 40 all
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17 questions