1.2b The PythagoreanTheorem1.2b The PythagoreanTheorem
1.2b The PythagoreanTheorem1.2b The PythagoreanTheorem
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Review: Right Triangles
•A triangle with a 90degree angle
•The hypotenuse is the longest side
•Area:
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Pythagorean Theorem:
•The Pythagorean theorem works only with RightTriangles
•Rule: Each side of a right triangle is used to make asquare
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Pythagorean Rule: {A2+B2=C2}
•Naming the sides of a right triangle:
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Proof of Pythagorean Theorem
•Given that the two rectangles have the same size
•This square is created by the hypotenuse, so it’sthe large square
•Move the triangles in the second square to createthe middle and small squares
•The area of the large square is equal to the sumof the two smaller squares
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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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Ex: Two buildings are 95meters apart. Building Ais 55m tall and the tower is 145m tall. A wire isconnecting both buildings. What is the shortestlength for this wire?
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Create a right triangle
Find the length of each side
Use the Pythagoreantheorem to find thelength of the wire
Ex: Two boats are sailing away from the sameport. The 1st boat sails West at 15km/hr, the2nd boat sails North at 22km/hr. How far arethe boats from each other after 2.5hours?
Port
X 00
0 0 0
X 0 0
0 0 0
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First find the distance that each will
boat travel
Boat A:
Boat B:
The distance creates a right triangle
Use the Pythagorean theorem to findthe length of the hypotenuse
Homework:
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