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geometry finals (semester 2) study guide :)
chapter 6  relating lines to planes
VOCAB 
plane  a surface such that if any two points on the surface are connected by a line, all points of the line are also on the surface. 
noncoplanar  not on the same plane. 
coplanar  on the same plane. 
foot  point of intersection of a line and a plane. 

POSTULATES 
Three noncollinear points determine a plane. 
If a line intersects a plane not containing it, then the intersection is exactly one point. 
If two planes intersect, their intersection is exactly one line. 

THEOREMS 
A line and a point not on the line determine a plane. 
Two intersecting lines determine a plane. 
Two parallel lines determine a plane. 
If a line is perpendicular to 2 distinct lines that lie on a plane and that pass through its foot, then it is perpendicular to the plane. 
If a plane intersects 2 parallel planes, the lines of intersection are parallel. 
chapter 8  ratio and proportion
THEOREMS 
MeansExtremes Products Theorem  a/b = c/d > ad=bc 
MeansExtremes Ratio Theorem  pq=rs > p/r=s/q etc. 
Arithmetic mean example: given 3 & 7, 3+27/2= 15 
Geometric mean example: given 3 & 7, 3/x = x/27 x=+ or  9 
AAA (angles)  similar 
AA (angles)  similar 
SideSplitter Theorem  ab/bc = ae/ed 

TERMS 
Dilation/Reduction 
Similarity  same shape but not size 
chapter 10  circles
TERMS 
concentric circle  same center with different size 
chord  points connected by a segment on a circle 
diameter/radius 
secants/tangents 

THEOREMS 
If a radius is perpendicular to a chord then it bisects it (reversed too). 
The perpendicular bisector of a chord passes through the center of a circle. 
If 2 chords are equidistant from the center then they are congruent (reversed too). 
secant/tangent theorems  example: 1/2 (large angle  medium angle) = small angle 
chords: ev . en = el . se 
tp (tangent) squared = (pr)(pq aka external part of secant) 
pb . pa (external part of secant) = pd . pc (external part of secant) 
chapter 12
TERMS 
bases 
lateral faces 
lateral edges 
slant height 
altitude (height) 
LA: Lateral surface area  no bases 
TA: Total surface area  with bases 
volume 


chapter 7  triangle application theorems
THEOREMS 
The sum of the measures of the 3 angles of a triangle is 180. 
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. 
A segment joining the midpoints of 2 sides of a triangle is parallel to the third side, and its length is onehalf the length of the third side (midline theorem). 
No choice theorem  if 2 angles of a triangle are congruent then the remaining ones are also. 
AAS  angle angle side 

FORMULAS 
sum of angles in polygon = (sides  2)180 
exterior angles = 360 
diagonals = sides(sides  3)/2 
exterior angle = 360/sides 
chapter 9  a lot of different things
RADICAL REVIEW 
squared root of 48 = 4 radical 3 
squared root of 5/3 = squared root of 15/3 

CIRCLES 
circumference  pi d 
area  pi r squared 
sector  fraction of circle area 
arc  fraction of circumference 
secants  through circle 
tangent  edge of circle (external/internal) 

RIGHT TRIANGLE ALTITUDES 
h squared = x . y 
a squared = x . c 
b squared = y . c 

OTHER 
pythagorean theorem  a squared + b squared = c squared 
distance formula  squared root (x2  x1) squared + (y2  y1) squared 
30 60 90 
45 45 90 
SOH CAH TOA 
chapter 11  area
I don't feel like writing all of the area formulas but here are the ones you need to know... 
square/rectanle 
triangle 
parallelogram 
trapezoid (and median) 
kite 
polygons 
circle, sectors, segments 

hero formula: squared root of s(sa)(sb)(sc) 

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