Download a location in space 1. A point has no length, no

Section 1.2
Mrs. Wilson
Points, Lines, and Planes
Name
Date
Point---a location in space
1. A point has no length, no width, and no thickness
2. A point is denoted by a capitol letter
3. All shapes in geometry are composed of one or more points
Block
A
“point A”
Line---an infinite set of points that extend in two directions without end
1. A line has no width and no thickness.
2. A line is denoted by two points contained in the line.
3. The textbook may also denote a line using a single lowercase letter.
Plane---an infinite set of points that creates a flat surface that extends without ending
1. A plane extends without ending, remaining flat.
2. A plane has no thickness.
3. A plane is denoted by three or four capitol letter contained in the plane.
4. Often planes are drawn as rectangles. However, they DO NOT have edges.
A
B
𝐴𝐵
A
B
D
C
Plane ABCD
Space---The set of all points
Collinear---Set of points on the same line
Non-Collinear---Points that cannot be contained in the same line
Coplanar---Points in the same plane
Non-Coplanar---Points that cannot be contained in the same plane
Section 1.3
Segment---A segment is named by its endpoints. X and Z are the endpoints of ̅̅̅̅
1. A segment has two definite endpoints.
2. ̅̅̅̅ and ̅̅̅̅ denoted the same segment.
3. A segment can be measured to find its length.
Ray---A portion of a line with one definite end point
1. A ray has one definite endpoint.
2. A ray is denoted using the endpoint first followed by another point
on the ray indicating the direction of the ray.
Opposite rays---Two rays continuing in opposite directions with a common endpoint
Length of a segment---“the length of ̅̅̅̅” is denoted as AB
X
̅̅̅̅
𝑋𝑍
Z
Segment Addition Postulate---If B is between A and C, then AB + BC = AC
Congruent---two objects with the same shape and size
If AB = CD, then ̅̅̅̅ ̅̅̅̅
Definition of a Midpoint---a point that divides a segment into two congruent segments
Definition of a Segment Bisector---A line, a ray, or a plane that intersects a segment at its midpoint
Section 1.4
A
Definition of an angle---A figure formed by two rays with a common endpoint
Denoted as
⃗⃗⃗⃗⃗ 𝑎𝑛𝑑 𝐵𝐶
⃗⃗⃗⃗⃗ 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑠𝑖𝑑𝑒𝑠
𝐵𝐴
B
Middle letter is always
the “vertex” of the angle
C
Angles may also be named using a numbers placed by the vertex.
A
𝐴𝐵𝐶 𝑐𝑎𝑛 𝑎𝑙𝑠𝑜 𝑏𝑒 𝑛𝑎𝑚𝑒𝑑
1
B
C
Measuring an angle---An angle is measured by the distance between the two sides, not the lengths of
the sides.
Classifications of angles
1. Acute-any angle less than 90˚
2. Right-any angle equal to 90˚
3. Obtuse-Any angle between 90˚ and 180˚
4. Straight-Any angle equal to 180˚
Note: You cannot determine an
angle is right based on the way it
looks!!!!!
Congruent Angles---Two angles with equal measures
Definition of an angle bisector---A ray that divides an angle into two congruent angles
If
is bisected by ⃗⃗⃗⃗⃗⃗ , then
Adjacent angles---Two angles that share a common side, but no common interior points
Angle Addition Postulate---If a point Y lies on the interior of <XOZ, then m<XOY + m<YOZ = m<XOZ
X
O
Y
Z
1
Section 1.5
Postulate 5
A line contains at least two points; a plane contains at least three points not all in one line; space
contains at least four points not all in one plane.
Postulate 6
Through any two points there is exactly one line.
Postulate 7
Through any three points there is at least one plane, and through any three noncollinear points, there is
exactly one plane.
Postulate 8
If two points are in a plane, then the line containing those two points is in that plane.
Postulate 9
If two planes intersect, then their intersection is a line.
Theorem 1-1
If two lines intersect, then they intersect in exactly one point.
Theorem 1-2
Through a line and a point not on the line, there is exactly one plane.
Theorem 1-3
If two lines intersect, then exactly one plane contains both lines.