Transcript File

Proof:
Conditional
Statements
Agenda:
1. Proof and The Axiomatic
System
2. Conditional Statements
3. Proving conditional
statements
4. Justification of
statements
5. Debrief
DO NOW 9/22:
Is the statement below true?
Explain/justify your answer.
“If 6x + 10 = 8x, then x = 5”
Proof: The Basics
 A proof is an argument, a justification, or a reason that
something is true. It is an answer to the question “why?”
when the person asking wants an argument that is
indisputable.
 There are three basic requirements for constructing a
good proof:
1. Awareness and knowledge of the definitions of the
terms related to what you are trying to prove.
2. Knowledge and understanding of postulates and
previous proven theorems related to what you are
trying to prove.
3. Knowledge of the basic rules of logic.
The Axiomatic System
“Between any two
points, you can draw a
straight line”
If B is between
A and C, then
AB + BC = AC
Points Planes
Lines
“Vertical
angles are
congruent”
Axioms/Postulates –
statements accepted to
be true without proof
Definitions – terms
generated to clarify or
make more consise
Undefined Terms – basic
terms accepted as
starting points
Theorems –
statements that
require proof
Rays
Line Segments
Conditional Statements
“If there is a forest fire, then fish will die.”
 The hypothesis is the information you are assuming
to be true. (“p”)
 The conclusion is what a proposal of what will follow
from the hypothesis. (“q”)
pq
Using Logic in Geometry Problems
Debrief
 Why is it important to have good notes and
understandings of definitions and postulates?
 How can logic help you solve equations?
 Is logic math? Why/why not?
Proof:
Inductive vs.
Deductive
Reasoning
Agenda:
1. HW Review
2. Inductive vs. Deductive
3. BBQ Logic Problem
4. Inductive Reasoning
Practice
5. Debrief
DO NOW 9/23:
Find the next term in the sequence:
Inductive vs. Deductive Reasoning
Inductive Reasoning
 Going from observed cases to a generalized rule.

Ex. I left home at 6:30 Monday, Tuesday and Wednesday, and
got to school at 7:15. Therefore, if I leave home at 6:00 on
Thursday, I will get to school at 7:15
Deductive Reasoning
 Going from a general rule to a specfic statement.

Ex. The bus always takes 45 minutes to get from my hourse to
school. Therefore, if I take the bus at 6:30, I will get to school
at 7:15
BBQ Logic Problem
Five students attended a BBQ and ate a variety of foods.
Something caused some of them to become ill.
 Jaida ate a hamburger, pasta salad, and coleslaw. She




became ill.
Kyle ate coleslaw and pasta salad but not a hamburger.
He became ill.
De’Vonte ate only a hamburger and felt fine.
Jalen didn’t eat anything and also felt fine.
Tiana ate a hamburger and pasta salad but no coleslaw,
and she became ill.
Use inductive reasoning to make a conjecture about which
food probably caused the illness.
Using Inductive Reasoning to Solve Problems
Debrief
(EXIT TICKET)
 What is the difference between inductive and
deductive reasoning?
Proof: Vertical
Angles
Agenda:
1. Two Column Proofs
2. Vertical Angles
3. Statements and
Justifications Jigsaw
4. Debrief
Parallel Lines
and a
Transversal
Agenda:
1. HW Review
2. Google Maps
3. Angles on Parallel Lines
4. Debrief