Geometry CONTENT EXAM

Acute Angle

Vertex Connected by two rays

Obtuse Angle

Greater than 90 less than 180

Reflex angle

Greater than 180 but less than 360

Supplementary Angles

90 + 90

Complementary Angles

Two angles that sum up to 90

Adjacent Angles

Share 1 vertex

Corresponding Angle

Same position along the same parallel line

Vertical Pairs

angles are opposite each other and share the same vertex

Finding the sum of the interior angles of a polygon

180(n-2)

How many diangonals across a polygon formula

n(n-3)/2

Kite

2 pairs of congruent sides

Rhombus

all 4 sides are congruent

Regular Pentagon

All Sides are congruent

Apothem

Center to the opposite side

Finding the Area of a Pentagon

1/2 ap

Similar Triangles

Same shape and Proportional

Corresponding Angles are

Congruent

Trapezoids has

1 pair of parallel sides

Area of a Trapezoid

1/2h(b1+b2)

Area of an Isoceles Trapezoid (2 sides Congruent)

Mh

Area of Rhombus

1/2 D1D2

Parrallelgram

Parallel sides are congruent

Area of a Rectangle

l * w

Perimeter of a Rectangle

2w+2l

Area of a Triangle

1/2 bh

Fast Area of an Equilateral Triangle formula

S^2sqrt3/4

If you have no height and given all 3 sides, use the semiperimeter formula for the area of a triangle

sqrtS(S-a)(S-b)(S-c)

Altitude of a Triangle

a perpendicular line segment from a vertex to the opposite side

Orthocenter

Where all 3 altitudes meet

Obtuse Triangle

only 1 obtuse angle

Centroid

The point where all 3 medians of a triangle meet

Acute Triangle

where all 3 interior angles are less than 90

Pythagorean Theorem

a^2+b^2=c^2

What makes triangles congruent

SAS

ASA

AAS

SSS

HL

Concentrix Circle

Circles share the same center

Area of Circle

pi r^2

Circumference of a circle

Pi d

Circumscribed

Polygon inside a circle

Central Angle

Same angle inside then same on the out

Inscribed Angle is

2 times the angle

Arc length

outer angle/360 pi d

Area of a sector

angle/360 pi r^2

Right triangles inscribed in a semicircle are

always right

Chord Chord Angle Formula

1/2(arc 1 +arc2)

Secant Secant/Secant Tangent

1/2(difference in arc)

Tangent Tangent (snow cone angle)

180=x+angle

Volume of Sphere

4/3 pi r^3

Surface Area of Sphere

4 pi r^2

Volume of Cylinder

pi r^2 h

Surface Area of Cylinder

2pir^2+2pirh

Volume of any Prism

pi r^2h

Surface Area of any prism

2B+2Ph

Volume of a cone

1/3 pi r^2 h

Surface Area of a Pyramid

#T 1/2bh+B

Circumcenter

the point where the three perpendicular bisectors of a triangle's sides intersect

Incenter

Where all angles are bisected

Formula for an ellipse

x^2/a^2 + y^2/b^2=1

Find the FOCI

a^2-b^2=c^2

Diagonals of a square are

Perpendicular Bisectors

Diagonals on a rectangle are not

90 degrees

The dashed line on the parabola is called?

Directrix

If the parabola is facing upwards what is the point that the graph is “looking at”

Focal Point

Standard Formula for a parabola with vertical axis of symmetry and a vertex at

(x-h)²=4p(y-k)

Compound Events

2 or more independent events

Dependent Events

Rely on the outcome

Mutually exclusive

events that cannot occur at the same time

Theoretical Probrability

In theory you should get something

Objective Probability

Formulaic

Subjective

Based on your own interpretation

AUB

Bring together

A∩B

What do they share

P(AUB) =

P(A) + P(B) - P(A∩B)

P(A|B)

P(A∩B)/P(B)

Odds in Favor

number of times event will occur / number times event will not occur

Odds Against

Not occur/ will occur

Ordinal Data

numerical order

Nominal Data

You cant put them in numerical order

Quantitative

measurement

Qualitatitve

Cant be measured using numbers

Discrete Data

Scatter plot, specific values

Continous Data

any value in the given range ex: temperature

Primary Data

Raw Data

Secondary Data

analyzed Data

Population

group/or collection everything

mean

average

mode

most often

median

middle

Range

Largest - Smallest

Permutations

nPr

Combinations

nCr

Excentrix Formula

e=c/a

Elispe centered at the orgin

x²/a² + y²/b²=1

Hyperbola centered at the origin

x²/a²-y²/b²=1

Airtmetic Sequence

a_n=a_1+d(n-1)

Geometric

a_n=a_1( r)^{n-1}

vertical asymptote

set the denominator equal to zero

horizontal asymptote

compare the degrees of the numerator and denominator of a rational function

N<D: y= 0

N=D: Then the fraction

N>D: none

Percent Error

Actual-Find/Actual

Percent Change

Difference/Original *100

Compound Continous Fomrula

Pe^{rY}