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1.3 Segments and their measures1.3 Segments and their measures
Schiewe 2004-5
Review of 1.1 and 1.2Review 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.Review cont.
Define the following symbols.AB, CD, GH, HGLine ABLine segment CDRay GH, G is the endpointRay HG, H is the endpoint
Defining POSTULATEDefining POSTULATE
1. 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).
2. A fundamental element; a basic principle.
3. Mathematics. An axiom. 4. A requirement; a prerequisite.
Now, Let’s define AXIOMNow, Let’s define 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.
Axiom
What’s up with 2 slides of What’s up with 2 slides of definitions – Judas Priest…definitions – Judas Priest…Postulates and axioms are fun-D-
mental 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 stuffNew 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…
ABAB, yes, that is right, , yes, that is right, ABABNo line on top, no No line on top, no nothing! Just the two nothing! Just the two points points AA and and BB written written next to each other. next to each other. ABAB Simply AB
The word betweenThe word 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!
between
Definitely, Definitely, NOT betweenNOT between
A B
C
Segment addition postulateSegment addition postulate
If B is between A and C, thenAB + BC = AC If AB + BC = AC, thenB is between A and C.
Finding distanceFinding distance
Find the horizontal distanceSquare that numberFind the vertical distanceSquare that number, too.Add those two squared numbersTake the square root, and then you
have DISTANCE
Distance between (1,6) and (4,10)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