Chapter 4 Flashcards
The union of two non-opposite rays with a common endpoint.
Angle
The two rays are ____
sides
The common endpoint is the _____
Vertex
The set of all points, P, in the plane of <BAC such that:
1. P and B are on the same side of line AC
2. P and C are on the same side of line AB
Interior of <BAC
The set of all points in the same plane that lie neither in the interior nor on the angle.
Exterior of <BAC
The union of the segments formed by 3 noncollinear points
Triangle
The points are _____
Vertices
The segments are ____
sides
an instrument used to measure angles
Protractor
The unit is _____
degrees
The number of degrees in an angle is its _____
Measure
To every angle there corresponds a real number between 0 and 180
Angle measurement postulate
The given number from the angle measurement postulate
Measure of an angle
Let ray AB be on the edge of half-plane, H. For every real number, r, between 0 and 180, there is exactly one ray AP with P in H such that the measure of angle PAB=R. (similar to point plotting theorem)
Angle construction postulate
if D is in the interior of angle BAC, then m<BAC=m<BAD+m<CAD. (similar to betweeness)
Angle addition postulate
If rays AB and AD are opposite and ray AC is any other ray, then angle BAC and angle CAD form a ____
Linear pair
angles whose sum is 180. each is a supplement of each other.
Supplementary angles
If two angle form a linear pair, they are supplementary
Supplement postulate
Angle < 90
acute
angle = 90
right
angle > 90
obtuse
angles whose sum is 90. Each is a complement of each other.
Complementary angles
angles whose measures are equal
Congruent
Two _____ are perpendicular if they are the sides of a right angle
rays
Two _____ are perpendicular if they contain a pair of perpendicular rays
lines
two _____ are perpendicular if:
1. each of them is a line, ray, or segment
2. they intersect
3. the lines containing them are perpendicular
sets
Perpendicular = _____
Right angle
a = a
reflexive
if a = b, then b = a
symmetric
if a = b and b = c, then a = c
transitive
a relation that is reflexive, symmetric, and transitive
equivalence relations
Congruence between angles is an equivalence relation
Theorem 4-1
