geometry finals (semester 2) study guide :)
chapter 6 - relating lines to planes
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.
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.
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
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
Similarity - same shape but not size
chapter 10 - circles
concentric circle - same center with different size
chord - points connected by a segment on a circle
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)
LA: Lateral surface area - no bases
TA: Total surface area - with bases
chapter 7 - triangle application 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
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
squared root of 48 = 4 radical 3
squared root of 5/3 = squared root of 15/3
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
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...
trapezoid (and median)
circle, sectors, segments
hero formula: squared root of s(s-a)(s-b)(s-c)