What is a conjecture?
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Transcript What is a conjecture?
1.3 Segments and their measures
Schiewe 2004-5
Review of 1.1 and 1.2
What is a conjecture?
An unproven statement based on
observation.
What do we call something which
proves a conjecture wrong?
A counterexample
Review cont.
Define the following symbols.
AB, CD, GH, HG
Line AB
Line segment CD
Ray GH, G is the endpoint
Ray HG, H is the endpoint
Defining POSTULATE
1.
2.
3.
4.
Something assumed without proof as
being self-evident or generally accepted,
especially when used as a basis for an
argument: “the postulate that there is
little moral difference between the
superpowers” (Henry A. Kissinger).
A fundamental element; a basic
principle.
Mathematics. An axiom.
A requirement; a prerequisite.
Now, Let’s define AXIOM
Axiom
L. axioma, Gr. ? that which is
thought worthy, that which is
assumed, a basis of demonstration,
a principle
a self-evident truth
An established rule, principle, or
law.
What’s up with 2 slides of
definitions – Judas Priest…
Postulates and axioms are fun-Dmental rules. Like 1 comes before
2… or geometry is so fun… or …
DISTANCE is always positive.
If you go from 2 to 5 or from 7 to 4,
you traveled a DISTANCE of 3 units,
DUHHHHHHHHHH. (understood)
Hey a postulate!!!!!
New Symbol – exciting stuff
We know how to denote line, line
segment, and ray.
Length of segment AB is easier than
all of these.
It is simply…
AB, yes, that is right, AB
No line on top, no
nothing! Just the two
points A and B written
next to each other.
AB
Simply AB
The word between
between
“Between” can only happen when all
3 points are collinear.
So,
–
A
B
C
B is between A and C because…
A, B, and C are collinear!
Definitely, NOT between
A
B
C
Segment addition postulate
If B is between A and C, then
AB + BC = AC
If AB + BC = AC, then
B is between A and C.
Finding distance
Find the horizontal distance
Square that number
Find the vertical distance
Square that number, too.
Add those two squared numbers
Take the square root, and then you
have DISTANCE
Distance between (1,6) and (4,10)
Horizontal distance = ?
4-1 = 3
Square that… 3x3 = 9
Vertical distance = ?
10– 6 = 4
Square that… 4x4 = 16
Add the two squared numbers. 9+16
= 25, square root of 25 = 5. Good d = 5