Geometric |
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Geometric |
|
Geometry began with the Egyptians and Babylonians thousands of years ago as a set of rules to compute simple areas and volumes. They used these to build their pyramids and to reestablish boundaries of land after the Nile rive would flood. By 600 B.C., Thales of Miletus, a Greek Mathematician, made a number of geometric conjectures. More importantly, he supported his conjectures with logical arguments. This method of building "chains of reasoning" by supporting conjectures with logical arguments was finally put into a single chain in The Elements, by Greek Mathematician Euclid. Starting with a set of facts regarded as true, called postulates, Euclid demonstrated systematically that from his previously verified conjectures that he could prove something new that also had to be true. You will use this same process for reasoning in this activity. This method of logic starts out with someone making many Observations that bring you to a place where you make generalizations about the patterns or repetitive things you see.
Observations |
Generalizations |
 |
|
80° + 55° + 45° = 180° |
Conjecture |
From this system of deductive logic you will build arguments to prove new conjectures based upon a collection of premises or accepted facts which in turn are based on given information or rules of congrunecy already established as fact. To begin builing a prior set of facts and premises you will first need to identify a few properties of Algebra, and then Properties of Equality.
| From the list of properties below, research, remember, find, or otherwise come up with a definition or example of the problem. Be sure to put these definitions into your own understandable words. Using a book definition is only good if you understand it. | |
| Properties of Algebra | Properties of Equality |
The Commutative
Property of Addition |
The Reflexive Property
of Equality |
Ways to connect and apply these properties. . .
1) When you state segment AC @ segment AC you are using what
property ? _______________________________
2) IF seg AC @ seg BD and seg BD @ seg
HK, then to say seg AC @ seg HK is supported by what ?
_____________
3) If x + 60 = 180, then x = 120 is supported by which property ?
_______________________________________
4) If 2(x + 14)=36, then x + 14 = 18 is supported by which property ?
____________________________________
5) If seg AC @ seg BD, then seg BD @ seg
AC is supported by which property ? ___________________________
