Chapter 2 Flashcards
Midpoint Formula
x1 + x2 y1 + y2
_______ , _______
2 2
Midpoint definition
The point that divides the segment into two congruent segments
Distance formula
(Square root around everything)
(x2 - x1) 2 + (y1 - y2) 2
Line segment definition
Segment A.B. consist of the endpoints A and B and all points on the line A.B.
that lie between A and B.
Ray definition
The ray AB, consists of the initial point A and all points on line AB that lie on the same side of A as B lies.
Opposite rays definition
On the line A.B. if C is between A and B, then, CA and CB are opposite rays
Collinear definition
Points, segments or Rays that lie on the same line
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 definition
An acute angle is an angle with a measure greater than 0° and less than 90°.
Right angle definition
Right angle is an angle with a measure of 90°
Obtuse angle Definition
An obtuse angle is an angle with a measure greater than 90° and less than 180°.
Straight angle definition
Straight angle is an angle that measures 180°
Interior of an angle
Every non-straight angle has an interior. point D is in the interior angle A If it is between points that lie on each
side of the angle.
Exterior of an angle
I agree non-Straight angle has an exterior. Point D is the exterior of angle 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 have no common interior points and lie on the same plane.
Adjacent angles definition (bullets)
- two angles
- share a common vertex
- share a common side
- have no common interior points
- lie on the same plane
Segment addition postulate
If B is between A and C then AB + BC = AC
Angle addition postulate
If C is in the interior of angle AOD, then m
Congruent segments
Two segments are congruent if they have the same length
Congruent angles
Two angles are congruent if they have the same measure
Midpoint
The point that divides the segment into two congruent segments
Segment bisector
A segment, Ray, line, or plane that intersects a segment at its midpoint.
Angle bisector
A ray that divides the angle into two congruent angles
Perpendicular lines
Two lines are perpendicular if they intersect to form a right angle
A line is perpendicular to plane….
If it is perpendicular to each line in the plane that intersects it
Through any two distinct points…
There exists exactly one line.
A line contains…
At least two points
Through any three noncollinear points…
There exists exactly one plane
A plane contains…
At least three noncollinear points
If two distinct points lie in a plane,
Then the line containing them lies in the plane
If two distinct planes intersect,
Then their intersection is a line
Addition property
If A = B, then A + C = B + C
Subtraction property
if A = B, then A - C = B - C
Multiplication property
If A = B, then AC = BC
Division property
if A = C and C doesn’t = 0
Then A / C = B / C
Reflexive property
For any real number A,
A = A
Symmetric property
Is A = B , then B = A
Transitive property
If A = B and B = C then
A = C
Substitution property
If A = B, then B can be replaced for A in any equation or expression.
Reflexive property of congruence
I need geometric object is congruent to itself. A is congruent to A
Symmetric property of congruence
If one object is congruent to a second, then the second object is congruent to the first.
A is congruent to B. b is congruent to A
Transitive property of congruence
If one geometric object is congruent to a second, and the second is congruent to a third, than the first object is congruent to the third object.
Vertical angles
Two angles are vertical angles if their sides form two pairs of opposite rays
Linear pair
Two adjacent angles are a linear pair if there noncommon sides are opposite rays
Complementary angles
Two angles are complementary if the sum of the measures is 90°. Each angle is the complement of the other
Supplementary angles
Two angles are supplementary and if the sum of their measures is 180°. Each angle is the supplement of the other
Linear pair postulate
If two angles are a linear pair, then they are supplementary, in other words, the sum of the measures is 180°
Congruent supplements theorem
If two angles are supplementary to the same angle or to congruent angles, then they are congruent
Congruent complements theorem
If two angles are complementary to the the same angle or to congruent angles, then they are congruent.
Vertical angles theorem
If two angles are vertical angles then they are congruent
