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Geometry Lesson 3.3A Monday, August 31, 2015
Geometry: Module 3 Lesson 3A
Bellwork: Explain 1: Use the definitions theorems and postulates learned so far to begin deductive logic. With a given bit of information, be able to make a logical next stepPractice 1: Worksheet (yellow)Presentations:
Explain 2: Practice proofsPractice 2: Worksheet (white) Closing:
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Nothing in math is used that cannot be ____________.
To prove things false, we use ______________ reasoning to provide a __________________.
To prove things true, we use ______________ reasoning to provide a formal proof.
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
1243
m
n
Step Reason1) Lines m and n intersect
<1 and <2 are a linear pair
<2 and <3 are a linear pair
2) 1) Given2) Definition of linear pair
3) m<1 + m<2 = 180 3) Linear Pair Theorem
4) m<1 = 180 m<2 4) subtraction property of equality
5) m<2 + m<3 = 180 Linear Pair Theorem5)
6) m<3 = 180 m<2 6) subtraction property of equality
7) (if m<1 = 180 m<2, and m<3 = 180 m<2)
m<1 = m<3 7) Transitive Property or Substitution
8) <1 ≅ <3 8) Definition of Congruence
Given: lines m and n intersect to form angles 1, 2, 3, and 4 (as shown)
Prove:
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
1) Definition of congruence
Examples)
Next)
Examples)
Next)
SG = TP
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
2) Definition of Midpoint
M is the midpoint of
Examples)
Next)
Point B is between A and B on a line and
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Examples)
Next)
•
•
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Examples)
Next)
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Examples)
Next)
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Examples)
Next)
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Examples)
Next)
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Properties and Possible Next Statements:
Examples)
Next)
Examples)
Next)
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Algebraic Properties:
Geometry Lesson 3.3A Monday, August 31, 2015
3.3ABegin UsingDeductiveLogic
Handout
Examples)
Next)
Examples)
Next)
Algebraic Properties:
