Bell Work:

A number cube is rolled once. What is the probability of rolling an even number? Express the probability as a fraction and as a decimal.

Answer:

½ , 0.5

Pythagorean Theorem

The longest side of a right triangle is called the hypotenuse. The other two sides are called legs. Notice that the legs are the sides that form the right angle. The hypotenuse is the side opposite the right angle.

Hypotenuse

Leg

Leg

Every right triangle has a property that makes right triangles very important in math. The area of the square drawn on the hypotenuse of a right triangle equals the sum of the areas of squares drawn on the legs.

Pythagorean Theorem: an equation that relates the sides of a right triangle in this way: the sum of the squares of the legs equals the square of the hypotenuse.

leg + leg = hypotenuse

2 2 2

We can use the letters a, b and c to show this in an easier way.

If a triangle is a right triangle, then the sum of the squares of the legs equals the square of the hypotenuse.

a + b = c

2 2 2

Use the Pythagorean Theorem to find the third side.

6 cm

8 cm

C

Answer:

6cm + 8cm = C

36cm + 64cm = C

100cm = C

C = 10cm

2 2 2

2

2

Find the measure of the missing side.

13 inches

12 inches

A

Answer:

A + 12 inches = 13 inches

A + 144 inches = 169 inches

A = 25 inches

A = 5 inches

2 2 2

2

2

The triangles we have considered so far have sides that are whole numbers. Three whole numbers that can be the side lengths of a right triangle are called a Pythagorean triple.

3, 4, 5

5, 12, 13

8, 15, 17

Multiples of Pythagorean triples are also Pythagorean triples. If we multiply 3, 4, and 5 by two, the result is 6, 8, and 10 which is a Pythagorean triple.

6 + 8 = 10

36 + 64 = 100

2 2 2

Are the numbers 2, 3 and 4 a Pythagorean triple?

Answer:

4 + 9 ≠ 16

Not a triple

The Pythagorean Theorem only applies to right triangles. If the sum of the squares of two sides do not equal the square of the hypotenuse then the triangle is not a right triangle.

Does a right triangle with the dimensions 8 cm, 9 cm, and 12 cm exist?

Answer:

No, although an 8, 9, 12 triangle exists, the triangle is not a right triangle because 8 squared plus 9 squared does not equal 12 squared.

Lesson 33:

Subtracting Integers

Recall that we use a method called algebraic addition to subtract integers. Instead of subtracting a number, we add its opposite.

Example:

Change each subtraction to addition and find the sum.

a) (-3) – (+2)

b) (-3) – (-2)

Answer:

a) (-3) – (+2) = (-3) + (-2) = -5

b) (-3) – (-2) = (-3) + (+2) = -1

Example:

Jocelyn has a checking balance of $1286. in the mail she receives a rebate check for $25 and a utility bill for $128. She deposits the rebate and writes a check for the bill. Write an equation with integers for the situation and find her checking balance after the transactions.

Answer:

Balance = 1286 + 25 – 128

Balance = 1286 + 25 + (-128)

= $1183

Addition and Subtraction with Two Integers

Operation

Rule

+

To find the sum of addends with different signs:

1. Subtract the absolute values of the addends

2. Take the sign of the addend with the greater absolute value

To find the sum of addends with the same sign:

3. Add the absolute values of the addends4. Take the sign of the addends

− Instead of subtracting a number, add its opposite

HW: Lesson 33 # 1-30

Due Tomorrow