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