Chapter 2: Lines & Angles Flashcards
Collinear points
points that lie on the same line
Noncollinear points
points that do not lie on the same line
Postulate 1: Two points determine
a unique straight line
Postulate 2: Three noncollinear points determine
a unique plane
Line segment
part of a line consisting of two points, called end points, and the set of all points between them
Congruent line segments
line segments that have equal lengths
Postulate 3: The Ruler Postulate: (a) To every point on line
there corresponds exactly one real number called its coordinate
Postulate 3: The Ruler Postulate: (b) To every real number
there corresponds exactly one point on the line
Postulate 3: The Ruler Postulate: (c) To every pair of points
there corresponds exactly one real number called the distance between the points
Postulate 3: The Ruler Postulate: (d) The distance between two points
is the absolute value of the difference between their coordinates
Betweenness of Points
If F,G, and H, are collinear, and if FG + GH = FH, then G is between F and H
Ray
A part of a line consisting of a given point, called the end point, and the set of all points on one side of the end point.
Angle
The union of two rays having the same end point. The end point is called the vertex of the angle; the rays are called the sides of the angle.
Congruent angles
angles that have equal measures
Postulate 4: The Protractor Postulate: (a) The rays in a half rotation (180 degrees) can be numbered
so that to every ray there corresponds exactly one real number called its coordinate
Postulate 4: The Protractor Postulate: (b) To every real number from 0 to 180
there corresponds exactly one ray
Postulate 4: The Protractor Postulate: (c) To every pair of rays there corresponds exactly one real number called
the measure of the angle that they determine
Postulate 4: The Protractor Postulate: (d) The measure of an angle is
the absolute value of the difference between the coordinates of its rays
Betweenness of Rays
(I cannot type a line with an arrow, so it will say “ray” instead)
(ray) PS is between (ray) PQ and (ray) PR if point S lies in the interior of <QPR.
Right angle
an angle with a measure of 90
Acute angle
an angle with a measure of less than 90
obtuse angle
an angle with a measure of greater than 90 (and less than 180)
midpoint of a line segment
the point that divides the line segment into two congruent line segments
Segment bisector
A bisector of (line) AB is any line, ray or line segment which passes through the midpoint of (line) AB.
Angle Bisector
(ray) OR is the bisector of <RON.
Addition Property: If equals are added to equals,
the results are equal: If a = b, then a + c = b + c
Subtraction Property: If equals are subtracted from equals,
the results are equal: If a = b, then a - c = b - c
Multiplication Property: If equals are multiplied by equals,
their products are equal: If a = b, then ac = bc
Division property: If equals are divided by nonzero equals,
their quotients are equal: If a = b, then a/c = b/c as long as c is not equal to 0
Substitution Property: If a = b, then either a or b may be substituted
for the other in any equation
Transitive Property: If two quantities are equal to the same quantity,
then they are equal to each other: If a = b and b = c, then a = c.
Reflexive Property
Any quantity is equal to itself: a = a.
Symmetric Property
The positions of the expressions on either side of an equals sign may be reversed: If a = b, then b = a.
