Chapter 2 Flashcards
Midpoint
The midpoint of a segment is the point that divides the segment into two congruent segments
Midpoint Formula
Midpoint=(x1+x2/2, y1+y2/2)
Distance Formula
Distance=√(x2-x1)2+(y2-y1)2
Line Segment
Line segment(symbol) AB consists of the endpoints A and B and all points on line (symbol)AB that lie between A and B
Ray
The ray AB, or AB(ray symbol), consists of the initial point A, and all points on line (symbol) AB that lie on the same side of A as B does
Opposite Rays
Two rays on the same line that share the same initial point and extend in opposite directions.
Collinear
Points, Segments, or rays that are on the same line are collinear
Angle
An angle consists of two different rays that have the same initial point. The rays are the sides of the angle and the initial point is the vertex of the angle
Acute Angle
An acute angle is an angle with measure greater than 0° and less than 90°
Right Angle
A right angle is an angle with a measure of 90°
Obtuse Angle
An obtuse angle is an angle with measure greater than 90° and less than 180°
Straight Angle
A straight angle is an angle that measures 180°
Interior of an Angle
A point D is in the interior of angle(symbol) A if it is between points that lie on each side of the angle.
Exterior of an Angle
A point D is in the exterior of angle (symbol) A if it is not on the angle or in the interior of the angle
Adjacent Angles
Two angles are adjacent if they share a common vertex and side, but no common interior points
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
Angle Addition Postulate
If B is in the interior of (angle symbol) AOC, then the (measure of angle symbol) AOB + (measure of angle symbol) BOC= (measure of angle symbol) AOC
Congruent Segments
Two segments are congruent if they have the same length
Congruent Angles
Two angles are congruent if they have the same measure.
Segment Bisector
a segment bisector is a segment, ray, line, or plane that intersects a segment at it’s midpoint.
Angle Bisector
an angle bisector is a ray that divides the angle into two congruent angles
Perpendicular Lines
Two lines are perpendicular if they intersect to form a right angle
Perpendicular Line and Plane
a line is perpendicular to a plane if it is perpendicular to each line in the plane that intersects it
Postulate 5
Through any two distinct points there exists exactly one line
Postulate 6
A line contains at least two points
postulate 7
Through any 3 noncollinear points there exists exactly one plane
postulate 8
A plane contains at least 3 noncollinear points
postulate 9
If two distinct points lie in a plane, then the line containing them lies in the plane
postulate 10
If two distinct planes intersect, then their intersection is a line.
Addition property of equality
if a=b, then a+c=b+c
Subtraction Property of equality
if a=b, then a-c=b-c
multiplication property of equality
if a=b, then ac=bc
division property of equality
if a=b and c does not equal 0, then a/c=b/c
reflexive property of equality
for any real number a, a=a
symmetric property of equality
if a=b, then b=a
transitive property of equality
if a=b and b=c, then a=c
substitution property of equality
if a=b, then a may be substituted for b in any equation or expression
reflexive property of congruence
for all objects A, A is congruent to A
Symmetric property of congruence
if A is congruent to B, then B is congruent to A
Transitive Property of congruence
If A is congruent to B, and B is congruent to F, then A is congruent to F
Vertical Angles
Two angles are vertical if their sides form two pairs of opposite rays.
Linear Pair of Angles
Two adjacent angles are a linear pair if their noncommon sides are opposite rays
Complementary Angles
two angles are complementary if the sum of their measures is 90°. Each angle is a complement of the other
Supplementary Angles
Two angles are supplementary if the sum of their measures is 180°. Each angle is a supplement of the other.
Linear Pair postulate
If two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180°
Congruent Supplements Theorum
If two angles are supplementary to the same angle or to congruent angles, then they are congruent.
Congruent Complements Theorum
If two angles are complementary to the same angle or to congruent angles, then they are congruent.
Vertical angles theorum
If two angles are vertical angles, then they are congruent.
