6/22/20161 2 Types of Triangles  Types by Length Equilateral Isosceles Scalene  Types by Angle Equilateral Right Obtuse Acute Equilateral Right Isosceles.

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Presentation transcript:

6/22/20161

2 Types of Triangles  Types by Length Equilateral Isosceles Scalene  Types by Angle Equilateral Right Obtuse Acute Equilateral Right Isosceles Scalene Equilateral Obtuse Acute

6/22/20163 Right Triangles  Legs Shorter sides of triangle  Hypotenuse Longer side of triangle Side opposite right angle Hypotenuse leg

6/22/20164 Pythagoras Born: about 569 BC in Samos, Iona, Greece Died: about 475 BC  Greek philosopher  Mathematician  Most Known For: Sum of Angles of a Triangle Pythagorean Theorem Constructing Figures of a Given Area and Geometric Algebra Discovery of Irrational #s The 5 Regular Solids Whole Number Ratios of Consonant Intervals Musica Mundana

6/22/20165 Pythagorean Theorem  If the triangle had a right angle (90°)... ... and you made a square on each of the three sides, then... ... the biggest square had the exact same area as the other two squares put together! Proof of the Pythagorean Theorem

6/22/20166 Pythagorean Example  The formal equation is: a 2 + b 2 = c 2 “a” and “b” are the two legs “c” is the hypotenuse  TRY THIS: a = 3 b = 4 c = 5 a 2 + b 2 = c = 5 2 Calculating this becomes: = 25 yes, it works !

6/22/20167 More Examples  Find c in : a 2 + b 2 = c 2 where a = 5 and b = = c = 169 c 2 = 169 c = √169 c = 13  Find b in : a 2 + b 2 = c 2 where a = 9 and c = b 2 = b 2 = 225 Take 81 from both sides b 2 = 144 b = √144 b = 12

6/22/20168 Pythagorean Triples  A "Pythagorean Triple“ a set of three numbers a,b,c such that a²+b²=c². Pythagoras proved that the sides of a right triangle have this relationship He then went crazy after discovering that the sides of a right triangle aren't always rational.

6/22/20169 Real - Life Application TV screens & computer monitors are measured on the diagonal

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