geometry terminology

3.12-3.13

if an angle’s vertex is on the arc and its sides terminate in the ends of the arc the angle is said to be?

inscribed in a segment or inscribed in an arc

major arc=

major segment

minor arc =

minor segment

the figure bounded by an arc of a circle and its chord

segment

an angle whose vertex is on the circle and whose sides are chords

inscribed angle

when is a tangent the limiting position of a secant?

when its two points of intersection coincide

usually means the length of the line from the exterior point to the second point of intersection

length of a secant

a straight line that cuts the circle in two points

secant

numerical measure of an angle =

numberical measure of its arc

a central angle is measured by its what?

intercepted arc,how big its arc is

common unit for measuring angles

angle degrees

unit for measuring arcs of a circle

arc degree

two magnitudes of the same kind which have no common unit of measure are said to be?

incommensurable

two magnitudes of the same kind which have a common unit of measure are said to be

commensurable

can be expressed as the ratio of two intergers

rational number

cannot be expressed as the ration of two integers and is a nonrepeating decimal

irrational

two magnitudes measured in the same units have the same?

ratio as their numerical measures

the number which tells how many times this magnitude contains the given units\

numerical measure

circles which have the same center

concentric circles

an angle inscribed in a circle is measured by one half its intercepted arc, however big the arc is the angle is half as much

theorem 42

all angles inscribed in the same segment or in congruent segments (or in equal arcs) are equal

corrollary 42-1

an angle inscribed in a segment whose arc is equal to a semicircle is a right angle

corollary 42-2

the only way to prove that a semi circle exists in a circle if we are not told we have one

a diameter of a circle bisects a circle into two semicircles

corollary 42-3

an angle inscribed in a segment whose arc is less than a semicircle is an obtuse angle.

An angle inscribed in a segment whose arc is greater than a semicircle is an acute angle.

when two circles intersect each other, the line of centers is the perpendicular bisector of the common chord

theorem 41