Axiomatic system

Examine the picture. If x is the hypotenuse of the triangle, how long does it measure?

(a)  

How many models can be used to illustrate axiomatic systems?

• Only one

• Two models

• Three models

• Cannot be determined

What is a THEOREM?

• An idea accepted or proposed as a demonstrable truth often as a part of a general theory

• A statement that is accepted to be true and does not need proof.

• the formation or expression of an opinion or theory without sufficient evidence for proof.

• a proposition that follows from one already proved.

What is a POSTULATE?

• An assumption that is common to all sciences that does not need proof.

• A statement exclusive to a particular science that does not need proof.

• A statement that is accepted to be false and does not need proof.

• An assumption that is accepted to be true and does need proof.

A period at the end of a sentence

• point

• line

• plane

What condition exists if an axiomatic system is independent?

• It can be proven from the other axioms.

• It cannot be proven from the other axioms.

• It is true based on the other axioms.

• It is false based on the other axioms.

In any triangle, the longest side is referred to as _______________.

• Elongated

• Ellipse

• Hypotenuse

• Hypothesis

Which theorem is being illustrated in the picture?

• Alternate Interior Angle Theorem

• Alternate Exterior Angle Theorem

• Same Side Interior Angle Theorem

• Pythagorean Theorem