1. 7.2 The Pythagorean Theorem
Review: Right Triangles
•A triangle with a 90degree angle
•The hypotenuse is the longest side
•Area:
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Side of a Square
•To find the side length of a square,take the square root of the area
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Pythagorean Theorem
•Each side of the triangle can be used to make asquare
•The sum of the small square and the medium squareis equal to the area of the large square
•Note: This is only works for Right Triangles
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Ex: Find the area of the missingsquare:
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Sides of a Right Triangle
•To find the length of a missing side
–Get the area of all 3 squares
–Square root the area of the square to find thelength of the side
Ex: Find the length of AC given the other sides
Find the area of each square
Square root the large square tofind the length of the hypotenuse AC
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Practice: Find the length of the missing side:
Find the area of each square
Square root the medium square tofind the length of AB
Find the area of each square
Square root the large square tofind the length of the hypotenuse AC
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Ex: Find the length of the diagonal
Draw 3 squares around
the triangle and find the areas
Find the area of the large square
Square root the area to find the length of the diagonal
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Challenge: Find the side length AB:
Draw a large square around the square
Find the area of square ABCD
Cut out the triangles in each corner
Area of square ABCD
Side Length AB is equal to the square root of the area
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