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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. |
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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. |
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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 |
Means-Extremes Products Theorem - a/b = c/d -> ad=bc |
Means-Extremes 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 |
Side-Splitter Theorem - ab/bc = ae/ed |
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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 |
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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 |
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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 one-half 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 |
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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 |
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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) |
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RIGHT TRIANGLE ALTITUDES |
h squared = x . y |
a squared = x . c |
b squared = y . c |
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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 |
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hero formula: squared root of s(s-a)(s-b)(s-c) |
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