TRIANGLES

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By: shreyasbpbp (5 month(s) ago)

very nice

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plz allow me to download ur ppt becoz I actually need it... N d work was just superb man

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Slide 1: 

TRIANGLES MADE BY; SARTHAK CHANANA X-B 37

INTRODUCTION : 

INTRODUCTION A TRIANGLE IS ONE OF THE BASIC SHAPES OF GEOMETRY WHICH IS DETERMINED BY ANY THREE NON COLINEAR POINTS.A TRIANGLE IS DETERMINED BY SIX PARTS THAT ARE THREE SIDES AND THREE ANGLES. BASED ON THESE THREE PARTS TRIANGLES CAN BE JUDGED OR CATEGORISED IN DIFFERENT GROUPS.LIKE IT CAN BE CALLED ACUTE,OBTUSE OR RIGHT TRIANGLE. STUDY OF TRIANGLES IS CALLED TRIANGLE GEOMETRY.BASED ON THIS STUDY VARIOUS PROPERTIES AND CHARACTERSTICS OF TRIANGLES ARE DISCOVERED BY GREAT METHAMATICIANS WHICH WILL BE DISCUSSED IN MY PPT ON “TRIANGLES”….

SIMILARITY OF TRIANGLES : 

SIMILARITY OF TRIANGLES SIMILARITY IS A CRITERIA TO JUDGE THE GEOMETRICAL FIGURES.ALL THE FIGURES WHICH ARE SAME TO EACH OTHER IN ANY WAY LIKE ANGLE, SIDE, ETC ARE SIMILAR. ALL THE TRIANGLES ARE SIMILAR TO EACH OTHER BY THEIR SHAPE. BUT OTHER THAN THIS SOME FACTORS MENTIONED ABOVE ARE USED TO CATEGORISE THEM IN SIMILAR FIGURES. THIS SIMILARITY IS THEN USED TO STUDY AND ESTABLISH RELATION BETWEEN TWO TRIANGLES.

TWO BASIC SIMILARITY RULES : 

TWO BASIC SIMILARITY RULES THERE ARE MAINLY TWO CONDITIONS THAT NEED TO BE FULFILLED FOR TWO TRIANGLES(OR ANY OTHER POLYGON) TO BE SIMILAR…. THERE CORRESPONDING ANGLES ARE EQUAL. THERE CORRESPONDING SIDES ARE IN SAME RATIO.

BASIC PROPORTIONALITY THEOREM : 

BASIC PROPORTIONALITY THEOREM THE THEOREM IS… “IF A LINE IS DRAWN PARALLEL TO ONE SIDE OF THE TRIANGLE TO INTERSECT THE OTHER TWO SIDES IN DISTINCT POINTS,THE OTHER TWO SIDES ARE DIVIDED IN SAME RATIO. ” IN THIS FIG. AD/DB=AC/EC

RESULT OF B.P.T : 

RESULT OF B.P.T THE THEOREM IS… IF A LINE DIVIDES ANY TWO SIDES OF A TRIANGLE IN SAME RATIO,THEN THE LINE IS PARALLEL TO THIRD SIDE. HERE THEREFORE,BC IS PARALLEL TO DE. AD/DB=AC/EC

CRITERIA FOR SIMILARITY OF TRIANGLES : 

CRITERIA FOR SIMILARITY OF TRIANGLES THERE ARE MAINLY THREE CRITERIA USED TO PROVE THE TWO TRIANGLES SIMILAR.. PROVE ALL SIDES SIMILAR(SSS) PROVE ALL ANGLES SIMILAR(AAA) PROVE TWO SIDES AND INCLUDED ANGLE SIMILAR(SAS)

AAA SIMILARITY CRITERIA : 

AAA SIMILARITY CRITERIA IF IN TWO TRIANGLES, CORRESPONDING ANGLES ARE EQUAL,THEN THEIR CORREPONDING SIDES ARE IN SAME RATIO AND HENCE THE TWO TRIANGLES ARE SIMILAR IN ABOVE FIG. <A=<A* <B=<B* <C=<C*. THEREFORE TWO TRIANGLES ARE SIMILAR BY AAA SIMILARITY CRITERIA

SSS SIMILARITY CRITERIA : 

SSS SIMILARITY CRITERIA IF IN TWO TRIANGLES SIDES OF ONE TRIANGLE ARE PROPORTIONAL TO THE SIDES OF THE OTHER TRIANGLE, THEN THEIR CORRESPONDING ANGLES ARE EQUAL AND HENCE THE TWO TRIANGLES ARE SIMILAR. HERE ALL SIDES OF 2 TRIANGES ARE PROPORTIONAL TO EACH OTHER.HENCE THEY ARE SIMILAR.

SAS SIMILARITY CRITERIA : 

SAS SIMILARITY CRITERIA IF ONE ANGLE OF A TRIANGLE IS EQUAL TO ONE ANGLE OF OTHER TRIANGLE AND THE SIDES INCLUDING THESE ANGLES ARE PROPORTIONAL,THEN THE TWO TRIANGLES ARE SIMILAR. IN THIS FIG. THE TWO TRIANGLES ARE SIMILAR BY SAS SIMILARITY . 10 8 4 5

AREA OF SIMILAR TRIANGLES : 

AREA OF SIMILAR TRIANGLES THE THEOREM IS…THE RATIO OF AREA OF TWO SIMILAR TRIANGLES IS EQUAL TO THE SQUARE OF AREAS OF THEIR CORRESPONDING SIDES. THE THEOREM IS…

PYTHAGORAS THEOREM : 

PYTHAGORAS THEOREM IF A PERPENDICULAR IS DRAWN FROM THE VERTEX OF THE RIGHT ANGLE OF A RIGHT TRIANGLETO THE HYPOTENUSE THEN TRIANGLES ON BOTH SIDES OF PERPENDICULAR ARE SIMILAR TO WHOLE TRIANGLE AND EACH OTHER…

PYTHAGORAS THEOREM : 

PYTHAGORAS THEOREM IN A RIGHT TRIANGLE THE SQUARE OF THE HYPOTENUSE IS EQUAL TO THE SUM OF SQUARES OF OTHER TWO SIDES. THIS MEANS:

USES OF TRIANGLES AND SIMILARITY IN OUR DAY_TO_DAY LIFE : 

USES OF TRIANGLES AND SIMILARITY IN OUR DAY_TO_DAY LIFE TRIANGLES ARE EVERYWHERE OR ANYWHERE . THEY ARE AN IMPORTANT PART OF OUR LIFE.MATHS IS INCOMPLETE WITHOUT TRIANGLES. THEY ARE USEFUL TO US IN MANY WAYS… TRIANGLES ARE IMPORTANT PART OF GEOMETRY. TRIGONOMETRY IS ENTIRELY BASED ON IT. ENGINEERING IS DEPENDENT ON USE OF TRIANGLES. THEY ARE BASIC BUILDING ELEMENTS OF OTHER STRUCTURES LIKE KITE,RHOMBUS ,ETC. USE OF SIMILARITY MAKES IT POSSIBLE TO STUDY THE FAR AWAY LOCATE OBJECTS BY ASSUMING THEM SIMILAR TO A FIGURE.

CONCLUSION : 

CONCLUSION FROM MY ANALYSIS I CONCLUDED THAT TRIANGES ARE AN ESSENTIAL PART OF HUMAN LIVES. GEOMETRY ARE INCOMPLETE WITOUT TRIANGLES.SIMILARITY IS AN IMPORTANT CRITERIA USED TO STUDY AND MAKE USE OF TRIANGLES. THIS TRIANGLES GIVE RISE TOTHINGS WHICH WE USE IN OUR DAY TO DAY LIVES WITHOUT EVEN NOTICING THEM. THANK YOU