Chapter 1: Points, Lines, Planes and Angles

34 terms by sophiasmith 

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Point

A position in space with no size, weight, or volume. A point is represented by a dot and symbolized by a capital letter.

Line

A straight set of points continuing indefinately in 2 directions. A line has no width, size or length. A line is represented by a double arrow with points and symbolized by naming two points or a single lower case letter as follows.

Plane

A flat surface extending indefinately in any direction. Planes have no thickness, size or weight. Planes are represented by parallelogram, and symbolized by one or more capital letters.

Space

set of all points

Collinear Points

Points on the same line

Coplanar

Points on the same plane

Segment

A part of a line between and including 2 endpoints. A line segment is symbolized by naming its two endpoints and placing a bar on top. Segment names are reversible, so they can be moved two ways.

Ray

A part of a line beginning at a point called the endpoint and continuing forever in one direction. It is symbolized by two letters, the first which MUST be the endpoint and the other is any point on the ray. Rays can have many names. (first letter of ray= endpoint)

Opposite Rays

Two rays with a common endpoint going in opposite directions.

Congruent segments

are segments that have the SAME LENGHT

Midpoint

of a segment is the point which divides the segment into two congruent parts

Bisector

of a segment is any line, ray, segment, or plane that passes through the midpoint of the segment

Number Line

is a way to represent lines, rays and segments while pairing points with numbers

Postulate 1: The Ruler Postulate

makes number lines

Postulate 2: Segment Addition Postulate

If B is between A and C, then AB + BC= AC

Acute Angle

an angle whose measure is between 0 and 90%

Right Angle

and angle whose measure is exactly 90 degrees

Obtuse Angle

an angle whose measure is between 90 and 180 degrees

Straight Angle

and angle who measure is exactly 180 degrees

Congurent Angles

Are angles that have equal measures

Adjacent Angles

are two angles in a plane that have a common vertex, common side, but no common interior points

Bisector of an ANGLE

is a line or ray that divides the angle into 2 congruent, adjacent angles

Postulate 3

The Protractor Postulate

Postulate 4: Angle Addition Postulate

If point B lies in teh interior of angle AOC, then angle AOB + angle BOC= angle AOC

Postulate

is a statement which can be accepted as true but can not be proven

Postulate 5

A line contains at least two points.
A plane contains at least three noncollinear points.
Space contains at least four noncoplanar points

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 non-collinear points there is exactly one plane

Postulate 8

If two points are in a plane, then the line that contains those points is in that plane.

Postulate 9

If two planes intersect, then their intersection is a line.

Theorem

statement that can be proven

Theorem 1

If two lines intersect, then they intersect at exactly one point

Theorem 2

Through a line and a point NOT in the line there is exactly one plane

Theorem 3

If two lines intersect, then exactly one plane contains the lines

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