Pythagorean Theorem.

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Presentation transcript:

Pythagorean Theorem

Pythagoras Pythagoras discovered that right triangles have a very special relationship. He found that if you square leg A and leg B, then add them together, you get the length of the hypotenuse squared. This can be represented by the formula:

Using a2+b2=c2

The Right Triangle Hypotenuse c Leg a Leg b Right angle

1. Square both legs 1 2 3 4 5 6 7 8 4 ft 9 10 11 12 13 14 15 16 3 ft 4ft a 1 2 3 4 5 6 3 ft b 7 8 9

2. Count the total squares 1 2 3 4 5 6 7 8 4 ft 9 10 11 12 13 14 15 16 3 ft 4ft 1 2 3 9 + 16 = 25 4 5 6 3 ft 7 8 9

3. Put that number of squares on the hypotenuse 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 3 ft 4 ft 4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16 9 + 16 = 25

Essential Question: How do I solve for a missing hypotenuse length using the Pythagorean theorem? Pythagorean Theorem

Key Points To solve for a missing hypotenuse: Step 1: Plug the numbers into the formula Step 2: Take the square of A & B Step 3: Add A & B Step 4: Take the square root Step 5: Check your work by plugging in your answer

Study Questions What is the inverse operation of squaring a number? What variables represent the legs?

Step One A=6 B=8 C=c Step one plug the numbers into the formula.

Step Two Step two, take the square of A and B.

Step Three Step three, add A and B.

Step Four Step four: Take the square root

Final Step The final step is to check your work. Check your work by plugging the answer back into the original formula to make sure the answer is correct.

Practice Find the length of the missing side. c 2.3 cm 5.1 cm

Practice Step One: Plug the numbers into the formula Step Two: Take the square of A and B Step Three: Add A and B Step Four: Take the square root

Practice a = 15, b = 20, c = ? a = 8, b = 10, c = ?

Practice a = 15, b = 20, c = 25 a = 8, b = 10, c = 12.81

Practice Find the length of the missing side. 10 m 6 m

Practice Step One: Plug the numbers into the formula Step Two: Take the square of A and C Step Three: Isolate b by subtracting 36 Step Four: Take the square root

Your turn 1) 2) 3)