• Before the bell rings...– Have your calculator– Have your covered textbook with you.

1. Is the solution correct? $80,800 – 8,088 = $72,822

2. Estimate the answer. 689 x 32 x 512 =

• Before the bell rings...– Have your calculator– Have your covered textbook with you.

1. Is the solution correct? $80,800 – 8,088 = $72,822

2. Estimate the answer. 689 x 32 x 512 =

No, $72,712

10,500,000

The Pythagorean Theorem

Section 9.3

P. 483

Essential Questions

• What is the difference between an irrational number and a rational number?

• How are real numbers and the Pythagorean Theorem used in everyday life?

• What types of real-life situations could the Pythagorean Theorem or square roots apply to? Why?

Pythagoras was born around 570 BC on the island of Samos

in ancient Greece. That is about 2,570 years ago!

Pythagoras

• He founded a school in southern Italy after traveling in Egypt and the Middle East. He was a philosopher, musician, and astronomer, but he is most remembered as a famous mathematician.

• The Egyptians knew that a triangle with sides 3, 4, and 5 make a 90o angle. As a matter of fact, they had a rope with 12 evenly spaced knots like this one:

• that they used to cut stones and build perfect corners in their buildings and pyramids. It is believed that they only knew about the 3, 4, 5 triangle and not the general theorem that applies to all right triangles.

• In any right triangle, the area of the square whose side is the hypotenuse (the side of the triangle opposite the right angle) is equal to the sum of the areas of the squares of the other two sides.

• The Pythagorean Theorem is one of the most important theorems in the whole realm of geometry.

• When the two shorter sides in a right triangle are squared and then added, the sum equals the square of the longest side or hypotenuse.

Pythagorean Theorem states:If a triangle is a right triangle, then a2 + b2 = c2

The converse states:

If a2 + b2 = c2, then the triangle is a right triangle.

The Pythagorean TheoremWhere c is the length of the hypotenuse and

a and b are the lengths of the other two sides, the theorem can be expressed as the following equation:

• c2 – a2 = b2

• c2 – b2 = a2

So, how could I find the

length of side “c”, the

hypotenuse?

42 + 32 =

16 + 9 = 25

Square root of 25 is 5.

4

3

C = ?

Find the missing side on each right triangle.

10 cm

24 cm

c2 = a2 + b2 c2 = 102 + 242

c2 =100 + 576 c2 = 676 c = 26 cm

c

5 in

12 in

c2 = a2 + b2 c2 = 52 + 122

c2 = 25 + 144 c2 = 169 c = 13 inches

17 ft 15 ft

a

c2 - b2 = a2 172 - 152 = a2

289 - 225 = a2

64 = a2

8 = a

12 in

b 37 in

c2 - a2 = b2 372 - 122 = b2

1369 - 144 = b2

1225 = b2

35 = b

Assignment• Page 484 #1-9

For each problem, write the formula, substitute and solve. (3 points per problem.)

• You may use a calculator. Round to the nearest tenth if needed.