congruent triangle by s. ramani. look at the followingfigures
TRANSCRIPT
CONGRUENT TRIANGLECONGRUENT TRIANGLE
BYBY
S. RAMANIS. RAMANI
LOOK AT THE FOLLOWINGFIGURES
WHAT IS CONGRUENT WHAT IS CONGRUENT FIGURE ?FIGURE ?
FIGURES HAVING SAME SIZE FIGURES HAVING SAME SIZE AND SAME SHAPE ARE SAID AND SAME SHAPE ARE SAID
TO BE CONGRUENT TO BE CONGRUENT FIGURESFIGURES
TO DEFINE CONGRUENT TO DEFINE CONGRUENT TRIANGLES WHAT ARE ALL TRIANGLES WHAT ARE ALL
REQUIRED?REQUIRED?
1.CONGRUENT LINES
2. CONGRUENT ANGLESWHY DO WE NEED ONLY THESE TWO?
SINCE SINCE TRIANGLESTRIANGLES ARE MADE ARE MADE UP OF UP OF LINESLINES AND ANGLES. AND ANGLES.
WHEN DO YOU SAY TWO LINES
ARE CONGRUENT?---WHY?
WHEN DO YOU SAY TWO ANGLES
ARE CONGRUENT?--WHY?
TWO LINES ARE TWO LINES ARE CONGRUENT IF THEY ARE CONGRUENT IF THEY ARE
OF IN SAME LENGTHOF IN SAME LENGTH
TWO ANGLES ARE TWO ANGLES ARE CONGRUENT IF THE ARMS CONGRUENT IF THE ARMS OF ONE ANGLE CONCIDE OF ONE ANGLE CONCIDE
WITH THE ARMS OF OTHER WITH THE ARMS OF OTHER ANGLEANGLE
WE TWO WHEN DO WE TWO WHEN DO TRIANGLES ARE TRIANGLES ARE CONGRUENT?CONGRUENT?
TWO TRIANGLES ARE SAID TWO TRIANGLES ARE SAID TO BE CONGRUENT IF WE TO BE CONGRUENT IF WE
SUPER IMPOSE ONE SUPER IMPOSE ONE TRIANGLE ON THE OTHER IT TRIANGLE ON THE OTHER IT
MUST COINCIDE EACH MUST COINCIDE EACH OTHEROTHER
WHEN TWO TRILANGLES WHEN TWO TRILANGLES ARE CONGRUENT WHAT ARE CONGRUENT WHAT
ARE ALL CAN BE ARE ALL CAN BE OBSERVED?OBSERVED?
1.THE SIDES ARE FOUND TO BE EQUAL
2.THE ANGLES ARE FOUND TO BE EQUAL
IDENTIFY THE SIDES ARE IDENTIFY THE SIDES ARE EQUAL AND THE ANGLES EQUAL AND THE ANGLES
ARE EQUAL.ARE EQUAL.
HOW MANY MATCHING PARTS FOUND ARE EQUAL?
THERE ARE SIX
GIVE FEW TRIANGLES TO IDENTIFY THE MATCHING PARTS ARE EQUAL
IS IT NECESSARY TO HAVE IS IT NECESSARY TO HAVE 6 MATCHING PARTS EQUAL6 MATCHING PARTS EQUALTO DEFINE TWO TRIANGLES TO DEFINE TWO TRIANGLES
ARE CONGRUENT?ARE CONGRUENT?
NONO
THEN HOW MANY?THEN HOW MANY?
IF POSSIBLE WITH LESS THAN 6 WHAT ARE THEY?
WHAT IS THE THEOREM?
SAS CONGRUENT THEOREMSAS CONGRUENT THEOREM
IF TWO SIDES AND AN ANGLE BETWEEN THE SIDES ONE TRIANGLECORRESPONDINGLY EQUAL TO TWO SIDES AND AN ANGLE BETWEEN THE SIDES OTHER TRIANGLE, THEN THE TRIANGLES ARE CONGRUENT