Post on 23-Dec-2015
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The Pythagorean Theorem
A2 + B2 = C2
The Pythagorean Theorem
Leg A
Leg B
Hypotenuse
Parts of a Right Triangle
The Pythagorean Theorem
Diagonals
Side
Parts of a Rectangle or Square
Side
Notice that 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 allmeet at a 90 degree angle.
The Pythagorean Theorem
Right
Acute
Obtuse
Categorized by angles
A triangle with one right angle
All angles less than 90
One angle more than 90
The Pythagorean Theorem
Equilateral
Isosceles
Scalene
Categorized by sides
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 sum of the squares of the other two
sides.
A2 + B2 = C2
The Pythagorean Theorem
Click to playanimation
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 QuestionWhat 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 also make this equation true.
(i.e. 6, 8, and 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 TheoremNow we can try a couple!
21
20
29
1.
5
12
13
2.
33
56
653.
7
24
254.
5.
48
55
74
Is this a righttriangle?
no
The Pythagorean Theorem
Now proceed to the worksheetand then the lesson assessment.
A2 + B2 = C2