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Postulates, axioms and Theorems

Page history last edited by Tae-Il Moon 13 years, 11 months ago

____(0-10 pts.) Explain the difference between a postulate, axiom and theorem.

 

-Postulate: Any rule that is accepted as true without the need of evidence. (Example: Ruler Addition Postulate)

 

-Axiom: [See Postulate, it is another way of calling it]

 

-Theorem: A rule that needs evidence to be accepted as true. (Example: Pythagorean Theorem)

 

 

____(0-10 pts.) Describe the Ruler Postulate. Give several examples.

The ruler postulate is a term given to the calculation of the distance of a line segment.  Let us say for example that you have points A and B.  It doesn’t matter if one or more of these points are negative or positive, you are simply looking for the length of the line segment between these points.   The formula is to simply subtract one point from the other to find the difference.  The result must be a positive number since you are only looking for the distance between the two points.

 

Examples:

 

1.

 

 

 The first point is (-2,1) and the second point is (2,1),

so the distance would be 4. AB= l-2-2l= l-4l= 4.

The length is 4.

 

 

 

 

 

 

 

 

 

 

2.

 

 

The coin shows that its length is from 3mm to 5.5mm.

5.5-3= 2.5mm.

The coin's length is 2.5mm long.

 

 

 

 

 

 

 

 

3.

 

 

 

The graph shows us two points : (2,4) and (8,4).

AB= l2-8l = l-6l = 6.

The length is six.

 

 

 

 

 

 

 

 

 

____(0-10 pts.) Describe the Segment Addition Postulate. Give several examples.

As we learned before, a postulate is any rule that is accepted as true without the need of evidence.  The Segment Addition Postulate is something that is obvious, so it's accepted as true.  It states the following:

 

The distance from A to B plus the distance from B to C will equal the distance from A to C.

Use this example to understand it better:

If you travel from school (A) to your house(B) and then from your house (B) to the mall (C), it will be the same distance as if you traveled straight from school (A) to the mall(C).

AB + BC = AC

use the diagram below to understand:

 

Examples:

 

1. A is between B and C. The measure of BA is 24, and the measure of AC is 46. What is the measure of BC?

 

 

 

2.  B is in between A and Z. The measure of AB is 72 and the measure of BZ is 20. What is the measure of AZ?

 

 

 

 

3. C is between B and D. The measure of BD is 12 and the measure of BC is 3. What is the measure of CD?

 

 

4. BC=44

 

5. AD=36

 

 

6. CD=17

 

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