Transcript Notes Section 2.

Geometry Notes
Section 2-1
What you’ll learn
How to make conjectures based on
inductive reasoning
 How to find counterexamples

Vocabulary
Conjecture
 Inductive reasoning
 Counterexample

Conjecture

An educated guess
Make a conjecture




Given: lines l and m are
perpendicular
Conjecture: lines l and m form
adjacent angles
Conjecture: lines l and m form
right angles
Conjecture: lines l and m form
congruent, adjacent angles
Inductive Reasoning

An argument using many examples to
support the conjecture

The process of inductive reasoning starts
with observation.
 You
observe data that leads you to believe
there is a pattern
 Your conjecture is based on this pattern
Counterexamples
A false example
 An example that contradicts the
statement
 An example that proves your
statement wrong

Use inductive reasoning to find the
next two terms in each sequence.
24
4, 8, 12, 16, _____,
_____
20
12.5 _____
6.25
 400, 200, 100, 50, 25, _____,
5/4
2
 1/8, 2/7, ½, 4/5, _____,
_____
 -5, 3, -2, 1, -1, 0, _____,
_____
-1
-1
72
60
 360, 180, 120, 90, _____,
_____
729
243 _____
 1, 3, 9, 27, 81, _____,
485
1457
 1, 5, 17, 53, 161, _____,
_____
91 _____
140
 1, 5, 14, 30, 55, _____,

True or False?
If false give a counter example. . .
 Given: m + y > 10, y > 4
 Conjecture: m< 6
 Is
Find
that
a acounterexample
true statement?if you think it’s
 wrong.
If not, why not?
 Conjecture: m< 6 so let’s try m = 7
 7 + 4* > 10
*remember: y > 4

11> 10
 This
is a true statement so our
counterexample just proved our conjecture to
be wrong.
True or False? If false give a counter
example. . .
 Given: AM = MP
 Conjecture: M is the midpoint of AP
 What might a counterexample look like?
 Does it say M is between A and P?
 No
M
 Given AM = MP, M
is not always the
mdpt of AP
A
P
True or False? If false give a
counter example. . .
Given: A(-4, 8), B(3,8), C(3, 5)
 Conjecture: ΔABC is a right triangle


How would you know if it is a right
triangle?
 Use
the distance formula to find AB, BC, and
AC
 Then see if those measures work in the
pythagorean theorem
True or False? If false give a
counter example. . .
Given: noncollinear points R, S, and T
 Conjecture: RS, ST, and RT form a triangle


We know through any two points there is a
unique line. . .
 RS,
ST, and RT would have to make a triangle
Have you learned?
How to make conjectures based on
inductive reasoning?
 How to find counterexamples?


Assignment: Worksheet 2.1