Download The Pythagorean Theorem

MPM1D
Ms. Kueh
The Pythagorean Theorem
_____________________ – The side opposite the 90˚ angle in a right triangle. It is also the
longest side in a right triangle.
Pythagorean Theorem: 𝑎2 + 𝑏 2 = 𝑐 2 , where 𝑎, 𝑏, and 𝑐 are the sides of a right triangle; 𝑐 is the
hypotenuse.
c
a
b
Do you think the Pythagorean Theorem would work if we used half circles instead of squares?
Hint: Remember the formula for a circle. What formula would you use for a half circle?
Example 1
The advertised size of a computer or television screen is actually the length of the diagonal of
the screen. A computer screen measures 30cm by 22.5cm. Determine the length of its diagonal.
Example 2
Jenna is changing a light bulb. She rests a 4-m ladder against a vertical wall so that its base is
1.4m from the wall. How high up the wall does the top of the ladder reach? Round your answer
to the nearest tenth of a metre.
Example 3
Calculate the area of the triangular sail on the toy sailboat.
11 cm
8 cm
For Fun! Fermat’s Last Theorem:
No three positive integers 𝑎, 𝑏, and 𝑐 can satisfy the equation 𝑎𝑛 + 𝑏 𝑛 = 𝑐 𝑛 for any integer
value of 𝑛 greater than two.
Challenge: A Pythagorean Triple is 3 positive integers that satisfy the Pythagorean theorem.
One example would be 3, 4, 5 because 32 + 42 = 52 . Find all the Pythagorean triples where the
smallest number out of the three numbers is 10 or less.
Homework: pg. 423 #(1a, 2a, 3a, 4a,) 6 – 12