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
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.
2
2
a+b=c
2
Use the Pythagorean Theorem to
find the third side.
C
6 cm
8 cm
Answer:
6cm + 8cm = C
2
2
2
36cm + 64cm = C
100cm = C
C = 10cm
2
2
Find the measure of the missing
side.
13 inches
A
12 inches
Answer:
2
2
2
A + 12 inches = 13 inches
2
A + 144 inches = 169 inches
2
A = 25 inches
A = 5 inches
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.
2
2
6 + 8 = 10
2
36 + 64 = 100
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
a)
(-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:
1. Add the absolute values of the addends
2. Take the sign of the addends
−
Instead of subtracting a number, add its opposite
HW: Lesson 33 # 1-30
Due Tomorrow