fi Flashcards
ways to determine a plane
3 noncolinear points
a line and a point not on the line
2 intersecting lines
2 parallel lines
if a line intersects a plane not containing it…
then the intersection is exactly one point
if 2 planes intersect…
their intersections is exactly one line
If a line is perpendicular to 2 lines thru the foot…
then it is perpendicular to the plane
If a line is perpendicular to a plane…
then it is perpendicular to every line thru the ft
a line is perpendicular to a plane if…
it is perpendicular to every one of the lines that pass thru its ft
A line and a plane are parallel if…
they do not intersect
two planes are parallel if…
they do not intersect
what are skew lines
non-coplanar, non-parallel lines
T/F: if a plane contains one of two skew lines, it contains the other
False
T/F: If a line and a plane never meet, they are parallel
true
T/F: If two parallel lines lie in different planes, the planes are parallel
False
T/F: If a line is perpendicular to two planes, the planes are parallel
true
T/F: If a plane and a line not in the plane are each perpendicular to the same line, they are parallel to each other
True
the measure of an exterior angle of a triangle is equal to
the sum of the measure of the remote interior angles
a segment joining the midpoints of 2 sides of triangle is…
parallel to the 3rd side and its length is 1/2 the length of the third side
If 2 angles of one triangle are congruent to 2 angles of a second triangle…
then the 3rd angles are congruent
(AKA NO CHOICE THEOREM)
pentagon
5 sides
hexagon
6 sides
heptagon
7 sides
octagon
8 sides
nonagon
9 sides
decagon
10 sides
dodecagon
12 sides
pentadecagon
15 sides
n-gon
number
regular polygon is
equilateral and equiangular
1 3
x a
— = —
y b
2 4
what are the means and what are the extremes
numbers referring to terms
means: 2nd and 3rd
extremes: 1st and 4th
if the product of a pair of non-zero numbers is equal to the products of another pair of non-zero numbers then…
either pair of numbers may be made the extremes and the other pair the means of a proportion
JUST REFER TO THE SLIDE SO THIS MAKES SENSE
corresponding angles of similar triangles are…
congruent
coresponding sides of similar triangles are…
proportional
the altitude is drawn to the hypotenuse of a right triangle then…
3 similar triangles are produced
concentric circles
share the same center
congruent circles
circles are congruent if they have congruent radii
chord
segment that joins any 2 points on the circle
diameter
chord that goes through the center of the circle
if a radius is perpendicular to a chord then…
it bisects the chord
If a radius of a circle bisects a chord then…
is it perpendicular to that chord
If a line is the perpendicular bisector of a chord then…
it passes through the center of the circle
If a line is the perpendicular bisector of a chord, then…
it passes through the center of the circle
If 2 chords of a circle are equidistant from the center, then…
they are congruent
If 2 chords of a circle are congruent, then…
they are equidistant from the center of the circle
minor arc
less than 180
major arc
greater than 180
central angle measure is equal to
the arc
what makes arcs congruent
equal length
If central angles congruent then arcs congruent then chords congruent
MEMORIZE THAT ^
measure of an arc from a fractional part
fraction times 360
secant
a line that intersects a circle at 2 points
tangent
a tangent line is perpendicular to the radius drawn to the point of tangency
tangent
*a line that intersects the circle at one point
a line perpendicular to the radius drawn to the point of tangency
if a line if perpendicular to a radius at its outer endpoint then it is tangent
tangent segment
only intercept one point
secant segment
has internal and external segments that make up one secant
if 2 tangent segments are drawn to a circle from an external point then…
those segments are congruent
internal common tangent
in between two circles
external common tangent
outside the 2 circles
external common tangent
outside the 2 circles
an inscribed angle is
half the measure of the arc
chord-chord angle
arc + arc/2
secant-secant angle, secant tangent angle, tangent, tangent angle
outer arc-inner arc/2
if 2 inscribed or tangent chord angles intercept the same arc, then…
they are congruent
tangent-tangent angle and its minor arc is 180
1/2(180-x)
inscribed angle meaning…
all vertices are on the circle
circumscribed
all sides are tangent to the circle
If a parallelogram is inscribed in a circle, it…
has to be a rectangle
the length of an arc is = to the circumference of it circle times the fractional part of the circle determined by the arc
is = to the circumference of it circle times the fractional part of the circle determined by the arc
a median of a triangle
divides the triangle into 2 triangles with equal areas
AAS
Angle angle side in this order to prove two triangles congruent
sum of the measures of angles in a polygon
(n-2) x 180
the n is referring to the number of sides
exterior angles of a polygon always equal…
360 degrees
number of diagonals in a polygon that can be draw in polygon is given by….
n(n-3)/2
each exterior angle measure is given by
E = 360/n
meaning of similar figures
same shape not same size
measures are equal
ways to prove similar triangles
AA, SSS, SAS
If a line is parallel to one side of a triangle and intersects the other sides it,
divides the 2 sides proportionally
LOOK AT NOTES
If 3 or more parallel lines are intersecting by 2 transversals,
the parallel lines divide transversals proportionally
LOOK AT NOTES
If a ray bisects an angle of a triangle,
it divides the opposite side into segments that are proportional to adjacent sides
LOOK AT NOTES
distance formula
square root of (x1 - x2)^2 + (y1-y2)^2
pythagorean triples
3-4-5
6-8-10
7-24-25
5-12-13
8-15-17
If 2 inscribed or tangent-chord angles intercept congruent arcs then
theyre congruent
find length of arc
arc (pir^2)
—
360
area of rectangle
b x h
area of square
s^2
parallelogram
b x h
area of triangle
1/2(b x h)
area of a trapezoid
1/2 h (b1 + b2)
area of a kite
1/2 d1 d2
area of equilateral triangle
s^2/4 x root 3
area of regular polygon
1/2 a p
area circle
pi r^2
find ratio is areas
A1/A2 = (S1/S2)^2
hero’s area of triangle
square root of s(s-a)(s-b)(s-c)
semiperimeter = s
area of cyclic quad
square root of (s-a)(s-b)(s-c)(s-d)
surface area of prisms
LA = area of faces
TA = LA + 2B(area of bases)
V = B x h
rectangular prism = l x w x h
surface area of cylinder
LA = 2pir (h)
TA: 2pir + 2(pir^2)
V = B (pir^2) x h
surface area of pyramids
LA: area of faces
TA: LA + B
V = 1/3 B x h
surface area of cone
LA: pi r l
TA: pi r l + pir^2
V = 1/3 B x h
surface area of a sphere
TA: 4pir2
V = 4/3pir^3
