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