Geometry: Circles and Spheres
If one angle is congruent to another angle and the two sides extending from the angle are proportional; then the triangle is similar
SAS Similarity Postulate
If three corresponding sides are proportional, than the triangles are similar
SSS Similarity Postulate
circumscribed circle
circle that has an inscribed polygon
C=2pr or C=pd
circumference of a circle
circumference
distance around a circle
hemisphere
half of the sphere; formed when the great circle seperates the two halves
the difference between 360 and all other arcs
measure of a major arc
measure of the central angle
measure of a minor arc
if two corresponding angles are congruent; then the triangles are similar
Angle-Angle Similarity Postulate
diameter
a chord that contains the center of a circle
diameter of a sphere
a chord that contains the center of a sphere
tangent
a line in the plane of a circle that intersects the circle in exactly one point
secant
a line that intersects a circle in two parts
inscribed polygon
a polygon is an ___ if all of its verticies lie on a circle
arc length
a portion of the circumference of a circle
radius of a sphere
a segment from the center to a point on the sphere
secant segment
a segment that contains a chord of a circle, and has exactly one endpoint outside the circle
chord
a segment whose endpoints are on a circle
chord of a sphere
a segment whose endpoints are on the sphere
radius
a segment whose endpoints are the center and any point on the circle
circle
a set of all points in a plane that are equidistant from a given point called the center
sphere
a set of all points in space equidistant from a given point; called the center
central angle
an angle whose vertex lies at the center of the circle
semicircle
an arc with the same endpoints as a diameter
arc
an unbroken part of a circle
inscribed angle
and angle whose vertex is on the circle and whose sides contain chords of the circle
semicircle
arc is 180
minor arc
arc less than 180
major arc
arc more than 180
A = pr^2
area of a circle
if corresponding angles are congruent and sides are similar
qualifications of similar polygons
S=4pr^2
surface area of a sphere
intercepted arc
the arc in the interior of an inscribed angle
great circle
the intersection of a shpere and a plane passing through the center of a sphere; *the circumference is the same as that of the sphere*
external segment
the part of the secant segment outside the circle
sector of a circle
the region bounded by two radii of the circle and their intercepted arc
congruent arcs
two arcs with the same measure that are arcs of the same or congruent circles
congruent circles
two circles with the same radius
V=4/3pr^3
volume of a sphere
segments of a chord
when two chords intersect in the interior of a circle, each cord is divided into two segements that are called ___
point of tangency
where the tangent hits the circle
