Geometry: Midterm formulas etc. Flashcards
area triangle
1/2bh
area rectangle
bh
area trapezoid
(b1+b2)h/2
area circle
pi(r)squared
area regular polygon
1/2(apothem x side)x(# of triangles)
complementary angles
two angles sum is 90
supplementary angles
two angles sum is 180
sum of interior angles
180(n-2)
sum of exterior angles
360
each interior angle of a regular polygon
180(n-2)/n
each exterior angle of a regular polygon
360/n
distance formula
d=square root of(x1-x2)squared + (y1 - y2)squared
midpoint formula
(x1+x2)/2 , (y1+y2/2)
slope formula
m=(y1-y2)/(x1-x2)
slope intercept form of a line
y=mx+b
point slope formula of a line
y-y1=m(x-x1)
distance from a point to a line
IAx+By+cI / square root of Asquared+Bsquared
pythagorean theorem
a(squared)+b(squared)=c(squared)
trig.
SOHCAHTOA
what does the measure of one exterior angle =
sum of 2 non-adjacent interior angles
what are ways to prove that triangles are congruent
ASA SSS SAS AAS HL
medium
goes from one vertex to the midpoint of the opposite side
altitude
goes from one vertex, perpendicular to the opposite side
perpendicular bisector
perpendicular to a side through the midpoint
angle bisector
cuts an angle in half
centroid
the intersection of the medians of a triangle
2/3 distance from each vertex to midpoint
incenter
the intersection of the angle bisectors of a triangle
circumcenter
the intersection of perpendicular bisectors of a triangle
orthocenter
the intersection of the altitudes of a triangle
converse
switch order
inverse
negate
contrapositive
flip and negate
law of detachment
p->q
p
q
law of contrapositives
p->q
~q->~p
law of disjunctive inference
pvq
~p
q
DeMorgan’s Law
~(PvQ)
~pA~q
Law of Modus Tollens
p->q
~q
~p
Chain Rule
p->q
q->r
p->r
axis of symmetry
-b/2a
what does a midpoint and a bisector do
splits a segment into 2 congruent parts
5 step process
state pair of congruent angles/segments
state second pair of congruent angles/segments
show segment addition/subtraction postulate
show that congruent’s added/subtracted from congruent’s are congruent
stated desired congruent segments by substitution
vertical angles
are congruent
right angles
are congruent
reasons to proof with angles:
complements
form right angles
complements of same angle are =
complements of =s <s are =
reasons to proof with angles:
supplements
form straight lines
supps of same < are =
supps of = <s are =
reasons to proof with parallel lines
alt. interior <s
2 lines II to same line then they are II
2 lines perpendicular to same line then they II
reasons to proof with perpendicular lines
form right angles
transversal is perpendicular to one of 2 II lines, then it is perpendicular to the other
