Download right triangle

THE PYTHAGOREAN THEOREM
2
2
2
A +B =C
THE PYTHAGOREAN THEOREM
PARTS OF A RIGHT TRIANGLE
LEG A
HYPOTENUSE
LEG B
THE PYTHAGOREAN THEOREM
SIDES
SIDES
DIAGONALS
PARTS OF A RECTANGLE
OR SQUARE
NOTICE TWO RIGHT TRIANGLES FORM A RECTANGLE
THE PYTHAGOREAN THEOREM
A RIGHT TRIANGLE HAS ONE ANGLE THAT
MEASURES 90 DEGREES.
A RECTANGLE AND Square
Have four sides that all
Meet at a 90 degree angle.
THE PYTHAGOREAN THEOREM
Categorized by angles
RIGHT
ACUTE
OBTUSE
A triangle with one right angle
All angles less than 90
One angle more than 90
THE PYTHAGOREAN THEOREM
Categorized by sides
EQUILATERAL
ISOSCELES
SCALENE
All sides equal (congruent)
Two sides equal (congruent)
No congruent sides
THE PYTHAGOREAN THEOREM
NOW FOR THE GOOD STUFF
THE PYTHAGOREAN THEOREM STATES THAT THE SQUARE OF
THE LONGEST SIDE OF A RIGHT TRIANGLE (HYPOTENUSE) IS
EQUAL TO THE SQUARES OF THE OTHER TWO SIDES.
A2 + B2 = C2
THE PYTHAGOREAN THEOREM
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THE PYTHAGOREAN THEOREM
PYTHAGORAS IS CREDITED WITH PROVING THIS
THEOREM; HOWEVER, THERE IS EVIDENCE THAT
BABYLONIAN MATHEMATICIANS USED OR KNEW
OF THE FORMULA LONG BEFORE PYTHAGORAS.
BIG QUESTION
WHAT CAREERS OR OCCUPATIONS USE OR COULD
USE THE PYTHAGOREAN THEOREM REGULARLY?
THE PYTHAGOREAN THEOREM
PYTHAGOREAN TRIPLES ARE THREE POSITIVE
INTEGERS THAT WHEN PLUGGED INTO THE
PYTHAGOREAN EQUATION, MAKE IT TRUE.
THE PYTHAGOREAN THEOREM
THE NUMBERS 3, 4 , AND 5 ARE PROBABLY THE
MOST COMMON PYTHAGOREAN TRIPLE. ANY
MULTIPLES OF THIS COMBINATION OF NUMBERS
ALSO MAKE THE EQUATION TRUE. I.E. 6,8, 10, ETC.
THE PYTHAGOREAN THEOREM
THE CONVERSE OF THE PYTHAGOREAN THEOREM
STATES THAT IF THE SQUARE OF THE LONGEST SIDE
OF A TRIANGLE IS EQUAL TO THE SQUARES OF THE
TWO LEGS OF A TRIANGLE, THEN THAT
TRIANGLE IS A RIGHT TRIANGLE.
THE PYTHAGOREAN THEOREM
NOW WE CAN TRY A COUPLE
21
29
1.
13
5
20
74
55
2.
12
33
48
Is this a right
Triangle?
65
3.
56
7
5.
25
4.
24
no
THE PYTHAGOREAN THEOREM
A2 + B2 = C2
NOW PROCEED TO WORKSHEET
AND THEN LESSON ASSESSMENT