sss theorem
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SSS THEOREM
Lucia Artigas9-2 20.3
OUTLINE2.
3. Introduccion to Theorems
4. Biography of Euclid creator of the SSS
5. Why Euclid creat The SSS
6. What is the SSS theorem?
7. Defenitions for understanding
8. Every day uses…
9. Examples 1
10. A Side Side Side Proof
11. Bibliogrfphy
INTRODUCCION TO THEOREMS
theorem (noun), theory (noun), theoretical (adjective): from
Greek theorema, fromtheorein "to look at," of unknown origin .
In mathematics, after studying a situation or a class of objects, a
person hopes to make speculations and then prove them, so
theorem came to mean the proof of a speculation that has been
arrived at by looking at something.
BIOGRAPHY OF EUCLID CREATOR OF THE
SSS
The Father of Geometry
Records show that he lived somewhere around 300 B.C. He was a Greek, most historians believe Euclid was educated at Athens. His teachers may have included pupils of Plato, who was a philosopher and one of the most influential The first printed edition of Euclid's works was a translation from Arabic to Latin, which appeared at Venice in 1482.
WHY EUCLID CREAT THE SSS
Euclid proved his Side-Side-Side (SSS) Theorem (I.8) and his
Angle-Side-Angle (ASA, diagram at the right) Theorem (I.26) in a
similar way. In SSS, if a triangle has all three sides conguent to the
corresponding sides of a second triangle, then they are congruent.
WHAT IS THE SIDE SIDE SIDE THEOREM?
The Side Side Side postulate states that if three sides of one
triangle are congruent to the three corresponig sides of another
triangle, then these two triangles are congruent.
DEFENITIONS FOR UNDERSTANDING
Def. Congruence: In Plane Geometry, two objects are congruent if all of
their corresponding parts are congruent
Def. Corresponding Parts: n. in congruent polygons (Triangles), the
pairs of sides which can be superimposed on one another.
Note: In the above, I used the term "congruent" instead of "equal"
when comparing sides and angles. Numbers are equal. Line segments
(sides) and angles are congruent. Calling them "equal" is a sloppy way
of saying that their measures (lengths or sizes)
EVERYDAY USES…
For Geometry Class with Miss H. in the subject of Math
If I want it to know if the 2 triangular windows are congruent
triangles, for it to be symmetric and nice to decorate my house .
To measure triangles faster because I know that if the sides are
equal they are congruent an their angles are congruent too, so i
don’t need to use a protractor an do every thing easier.
ABC XYZ
Alll 3 sides are congruent• ZX = CA (side)• XY = AB (side)• YZ = BC (side)
Therefore, by the Side Side Side postulate, the triangles are congruent
Example 1
A SIDE SIDE SIDE PROOF
Midpoint
RFERENCES
1.
http://www.cut-the-knot.org/WhatIs/WhatIsTheorem
.shtml
E. J. Borowski & J. M. Borwein, The Harper Collins
Dictionary of Mathematics, Harper Perennial, 1991
2.
http://www.mathwarehouse.com/geometry/congruen
t_triangles/side-side-side-postulate.php
Bibliogrfphy
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