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Acute angle is
Angles that measure less than 90° are called

Obtuse angles is ....
Angles that measure more than 90°

A right angle always measures...
 exactly 90° and indicated by a little square where
 the angle measure is

40 + n = 180 degress = straight line

Complementary Angles  because they add up to 90°.

Supplementary Angles, because they add up to 180°.

 Angles 1, 4, 5, and 8 are equal to one another.
 2, 3, 6, and 7 are equal to one another.
 The sum of any two adjacent angles, such as 1 and 2 or 7 and
 8, equals 180º
 Corresponding angles; Tranversal line intersects

 When two lines intersect, the angles that lie opposite each other,
 called vertical angles, are always equal.

Angles in a triangle equals...
180 degrees

 An equilateral triangle has three equal sides and three equal
 angles

 An isosceles triangle has two equal sides and two equal angles
 Notice that the two equal angles are the ones opposite the two equal
 sides

A triangle with no equal sides and angles ...
Scalene

 The exterior angle of a triangle plus the interior angle
 with which it shares a vertex is always 180°. The exterior angle is
 also equal to the sum of the measures of the remote interior angles.

 rule of sides
 x is greater than the difference of the sides (104= 6)
 but less than the addition of the sides (10+4 = 14)

 side a is the longest side and A is the largest
 angle.
 side c is the shortest side and c is smallest angle.

Pythagorean theorem is
 a^{2 }+ b^{2 = }c^{2}
 3^{2 }+ b^{2 = }5^{2}
 9 25 = b^{2}
 16 = b^{2} = b = 4

what are pythogoream's triples?
 {3, 4, 5}
 {5, 12, 13}
 {7, 24, 25}
 {8, 15, 17}
 therefore z would be 5 x 10 = 50

how do know x and the value of the angles inside?
 pythagoream ratio: s:s: s√2
 therefore x = 5√2

 30 60 90 triangle means ratio is s:s√3:2s
 therefore 1:2:1√3

Area of a Triangle is ?
1/2 x base x height

What is the total degrees inside a sqaure?
360

area of a square (2 formulas)
 base x height
 1/2 diagonal ^{2}

area?
 2 equal sides and 2 equal sides
 all right angles
 area = length x width

area?
 area is base x height
 2 and 2 sides not necessarily right angles

 BE= ED and AE = EC
 ∆ABD = ∆BCD
 ∆AEB = ∆DEC and ∆BEC = ∆AED

area?
 1/2d^{1} x d^{2}
 or base x height

area?
area = 1/2 (b^{1} + b^{2}) x h

Formula to calcuate degrees in polygons (all equal sides) and average for angle
(n2) 180 = total degrees
for average divide by number of sides (n)

triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon... how many sides for each?
3, 4, 5, 6, 7, 8, 9, 10, 12

volume of a rectangle?
l x w x h

surface area of a rectangle?
 2lw + 2lh +2wh.

volume and surface area of cube?
 Volume = s^{3}
 sa = 6s^{2}

volume and surface area?
 volume =πr^{2}h
 surface are = circumference x h x 2area of circle
 circumference = 2πr
 area= πr^{2}

circumference?
perimeter of a circle : 2πr

Area of a circle is ?
area = πr^{2}


 AB = chord
 tangent lines
 central angle = cuts arch at same angle

 An inscribed angle will always cut out an arc in the circle that
 is twice the size of the degree of the inscribed angle. For example, if
 an inscribed angle is 40º, it will cut an arc of 80º in the circle.

a central angle in an inscribed angle will be twice the size

AB?
 arc length =
 need c = 60
 AB is twice because it is an inscribed angle
 120/360

area of sector?
 central angle so 70/360

If 2x + 3y = –6 and –4x + 16y = 13,
what is the value of y?
can add or subtract equations, if variables do not cross out think about mulitpling or dividing each side of one equation by the same number

base to a power of 0 equals?
1

number to a negative exponent means?
X^{4}
1/X_{4}

x^{2}+2xy +y^{2} = ????
x^{2} +6xy + 9

x^{2} – 2xy + y^{2
}x^{2}–10xy + 25
 (x –y )( x – y) = (x –y)^{2}
 (x –5)^{2}

(x +y)(x – y)
(x + 4)(x – 4)

ratios:
we are told ratio of boys to girls are 4 to 5 and there are 12 boys in the classes, how many girls are there?
 boys = boys 4 = 12 4x = 12 x5 x= 60/4
 girls girls 5 x
x= 15

Probability formula?
In a bag containing 12 red, 13 white, and 15 black marbles, what is the probability of selecting a red marble on a single draw?
 number of desired outcomes
 total number of possible outcomes
12/12+13+15 = 12/40 = 3/10

distance formula?
rate x time = distance

work formula
If you knit 2 sweaters per hour, and knit for 8 hours
 rate x time
 2 per hour x 8 hours = 16

What is a prime number?
 positive number; divideable by itself and one other number only
 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
 61, 67, 71, 73, 79, 83, 89, and 97
 solution : estimate square of number and then check all number below that number
 97 = 10 = check 2, 3, 5, 7,

How to add or subtract fraction?
need common denominator and numerators are added together or subtracted

Multiplying fractions?
4 x 1 x10
5 8 11
 numerators times and denominators
 cancelling out = if any numerators are can be divided by the same number as a denominator
 4 and 8 divide by 4 and 5 and 10 divide by 5
 1 x 1x2 / 1 x 2 x 11

Divide fractions?
1 x 4
2 5
 all you have to do is flip the second fraction and then multiply
 5
 8

ratios?
For every 40 games a baseball team plays, it loses 12 games. What is the ratio of the
team’s losses to wins?
red, blue, and green marbles ratio of 5:4:3, and he has a total of 36 marbles. How many blue
marbles?
40  12 = won 28 games = 12:28 = 3:7
 5 + 4 + 3 = 12 = 36/12 = 3 times each by 3 to find how many
 5

Percentages
4 is what percent of 20?
What percent of 2 is 5?
 4 = 20x = 400 =20x = 20%
 100
5 = 2x/100 = 2x = 500 = x = 250%

To convert .3875 into a fraction
 delete decimal and has four digits after the decimal point, put four
 zeros in the denominator following the number 1:
 3875/10000 and reduce

percentage increase or decrease
Sam pays $1.65 for a banana that was originally priced at $2.00
Sam pays $2.00for a banana that was originally priced at $1.65
 percentage increase
 percentage decrease
% increase or decrease = # increase or decrease divide by original number

Exponents
Adding or subtacting?
multiplying?
Dividing?
factions to an exponent 1 to the exponent 3
2
 need to be same base 2x^{2 }+ 3x^{2}
 add exponents together
 dividing subtracting exponents
 1x1x1 over 2x2x2

roots
multiple and divide

roots
single number under a radical sign can be split into two numbers whose product is the
original number

average if do not have all numbers
average of class marks is 74. B got 50%; C got 60%; D got 90% and E got ??
 average = sum divide by number of terms
 74 = 50 + 60+ 90 + x divided by 4

Interest
principle x rate x time

Median?
 median of a group of numbers is the middle term when the numbers are written in either ascending or descending order.
 if two numbers are in the middle you take the mean (average) of two numbers

mode
number that occurs most frequently

range?
difference between the largest term and the smallest term

