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The Pythagorean Theorem
Objective: Find the length of a missing side using the Pythagorean Theorem.
Interesting fact:
“The name of Pythagoras was selected for this theorem not because he discovered it -- the Pythagorean theorem or Pythagorean triples had been in use for centuries. -- but perhaps because Pythagoras was the first to prove the theorem.”
Mini Lab 1. Find the area of each square.
2. Use grid paper to cut out three squares with sides 3, 4, and 5 units.
3. Form a right triangle with these squares. Compare the sum of the areas of the two smaller squares with the area of the larger square.
• We use the Pythagorean Theorem when we want to know the remaining length of the side of a right triangle for which we already know two lengths.
• In a right triangle the 2 sides that form the right triangle are called legs.
• The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle.
• The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the length of the legs.
The Pythagorean Theorem states:
In a Right Triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
a2 + b2 = c2
Example: Find the missing side in each right triangle.
a2 + b2 = c2
32 + 42 = C2
9 + 16 = C2
25 = c2
5 = C
Steps to find the
hypotenuse:
1. Use the Pythagorean
theorem.
2. Replace a and b with their
respective numbers: a with
3 and b with 4.
3. Square 3 and 4.
4. Add
5. Find the square root.
Example 2: Find the missing side in each right triangle.
Steps:1.Use Pythagorean
Theorem.2. Replace a with 6 and c
with 10.3. Square 6 and 10. 4.We “undo” the addition. We do this by subtracting
36 from each side.5.Solve.6.Find the square root.
a2 + b2 = c2
62 + b2 = 102
36 + b2 = 100-36 - 36 b2 = 64 b = 8
Videos we saw in class:
https://www.youtube.com/watch?v=uaj0XcLtN5c
https://www.youtube.com/watch?v=OluCdrAXje4
Homework: Find the missing side in the right triangle.
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