What is a conjecture? Download

Transcript
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