21 Triangles - 22 circles - 23 trig Flashcards
confusing concept
for any triangle, the sum of any two sides must be
greater than the third
technique
the golden rule of geometry problem is
to draw a picture
key formula
Pythagorean theorem
a^2 + b^2 = c^2
key formula
common triples right triangles:
3-4-5
6-8-10
5-12-13
7-24-25
8-15-17
key formula
special right triangles
45-45-90
30-60-90
key formula
45-45-90
x^2 + x^2 = (x√2)^2
key formula
30-60-90
x^2 + (x√3)^2 = (2x)^2
confusing concept
when two triangles have the same angles measures
their sides are proportional
key formula
π radians =
180 degrees
key formula
area of a circle
πr^2
key formula
circumference of a circle
2πr
key formula
arc length
2 π r (θ/360°)
key formula
area of a sector
πr^2 (θ/360°)
confusing concept
central angles have the same measure as
the arcs that they “carve out”
confusing concept
inscribed angles are half the measure of
arcs that they “carve out”
key formula
angles inscribed in a semicircle are always
90 degrees
confusing concept
a radius drawn to a line tangent to the circle is
perpendicular to that line
key formula
general equation of a circle in the xy-plane
(x - h)^2 + (y - k)^2 = r^2,
where (h,k) is the center of the circle and r is the radius
key formula
sin x
opposite/hypotenuse
key formula
cos x
adjacent/hypotenuse
key formula
tan x
opposite/adjacent
confusing concept
trigonometric functions are
ratios
confusing concept
sin 30 is always equal to
1/2
because all right triangles with a 30 degree angle are similar
key formula
SOH-CAH-TOA
sin, cos, tan
