7.4 Proving thePythagorean Theorem7.4 Proving thePythagorean Theorem
7.4 Proving thePythagorean Theorem7.4 Proving thePythagorean Theorem
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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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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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Pythagorean Rule: {A2+B2=C2}
•Naming the sides of a right triangle:
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Finding the missing sides:
Ex: Use the Pythagorean Theorem to find thelength of the missing sides to 2 decimal places:
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Practice: find the length of the missingsides for each right triangle
12cm
6cm
4cm
5cm
A
G
Challenge: Given EF = 4, FG = 8, & AE = 6.
Find the length of AG, to 2 decimal places,
D
B
E
F
H
First use ΔADC to find the length of AC
A
G
C
Next use ΔACG to find the length ofAG (Note ΔACG is a right triangle
C
Length of a Line Segment:
•Use the line segment to draw a square
•Use the area of the square to find the length ofthe line segment
•EX: Draw a square with the following lines
Adjacent lines in a square are perpendicular toeach other!!
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Use the triangles in the corner to draw theother sides
Practice: Find the length of the line segments:
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Draw a square with the
following line
Find the area of the square
Root the area to find the length
Homework:
•P104 to 105
–3, 5, 6, 9, 10, 11, 12, 15, and 16