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theorems for congruent triangles

theorems for congruent triangles

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  • 1. SSS THEOREM Lucia Artigas 9-2 20.3
  • 2. OUTLINE2. 3. Introduccion to Theorems4. Biography of Euclid creator of the SSS5. Why Euclid creat The SSS 6. What is the SSS theorem? 7. Defenitions for understanding8. Every day uses…9. Examples 110. A Side Side Side Proof11. Bibliogrfphy
  • 3. INTRODUCCION TO THEOREMS theorem (noun), theory (noun), theoretical (adjective): fromGreek theorema, fromtheorein "to look at," of unknown origin . In mathematics, after studying a situation or a class of objects, aperson hopes to make speculations and then prove them, so theoremcame to mean the proof of a speculation that has been arrived at bylooking at something.
  • 4. BIOGRAPHY OF EUCLID CREATOR OF THE SSS The Father of Geometry Records show that he livedsomewhere around 300 B.C. He was aGreek, most historians believe Euclid waseducated at Athens. His teachers may haveincluded pupils of Plato, who was aphilosopher and one of the mostinfluential The first printed edition ofEuclids works was a translation from Arabicto Latin, which appeared at Venice in 1482.
  • 5. 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 similarway. In SSS, if a triangle has all three sides conguent to thecorresponding sides of a second triangle, then they are congruent.
  • 6. WHAT IS THE SIDE SIDE SIDE THEOREM? The Side Side Side postulate states that if three sides of one triangleare congruent to the three corresponig sides of another triangle, thenthese two triangles are congruent.
  • 7. DEFENITIONS FOR UNDERSTANDING Def. Congruence: In Plane Geometry, two objects are congruent if all oftheir corresponding parts are congruent Def. Corresponding Parts: n. in congruent polygons (Triangles), the pairsof sides which can be superimposed on one another. Note: In the above, I used the term "congruent" instead of "equal" whencomparing sides and angles. Numbers are equal. Line segments (sides) andangles are congruent. Calling them "equal" is a sloppy way of saying thattheir measures (lengths or sizes)
  • 8. EVERY DAY USES…  For Geometry Class with Miss H. in the subject of Math If I want it to know if the 2 triangular windows are congruenttriangles, for it to be symmetric and nice to decorate my house . To measure triangles faster because I know that if the sides areequal they are congruent an their angles are congruent too, so i don’tneed to use a protractor an do every thing easier.
  • 9. Example 1 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
  • 10. A SIDE SIDE SIDE PROOF Midpoint
  • 11. RFERENCES Bibliogrfphy1. http://www.cut-the-knot.org/WhatIs/WhatIsTheorem.shtml E. J. Borowski & J. M. Borwein, The Harper Collins Dictionary of Mathematics, Harper Perennial, 19912. http://www.mathwarehouse.com/geometry/congruent_triangles/side- side-side-postulate.php