Chapter 1 notes  Hit Counter

Section 1.2 Points, Lines, and Planes

Point—a single location in space, has no dimension, usually represented by a small dot and named with a single capital letter. 

 

Line—an unending row of points extending in one dimension, usually represented by a straight line with arrows on both ends and named by two points on the line.        

     named  

 

 

Collinear Points—points on the same line. Noncollinear points are not on the same line.

 

Plane—a flat surface that extends in two dimensions like an unending floor or wall.

 

Coplanar Points—points on the same plane.  Noncoplanar points are not on the same plane.

 

Line Segment (or Segment)--a measurable row of points with two ends.

Segments are written as

Endpoints—the points at the ends of a segment. (in this case A and C)

 

 

Ray--a part of a line with one endpoint (aka the initial point).  

A ray is named using the endpoint and one additional point on the ray. 

 

Section 1.3  Measuring Segments

Distance between points—also known as the length of the segment connecting the points.

 

Distance on a number line can be found by taking the absolute value of the difference of the coordinates.

 

 

  Segment Addition Postulate

If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC

 

 

 

 

 

Between--a point, B is between two other points, A and C, only if it is on the segment connecting those two points.

 

 

Example:  D is between E and F.  ED = 10, EF = 30, DF = _______.

 

 

Example2:  F is between G and H.  GF = 2x + 1, FH = 6x, GF = 11.
 Find GH=_____.

 

 

Congruent segments--two or more segments with the same measure. (they are the same length)

 

 

 

 

 

 

Section 1.3 Distance and Midpoints

 

Distance on a coordinate plane can be found using the distance formula
The Distance formula

Or you can use the pythagorean theorem to find the distance.
The Pythagorean Theorem 

The Midpoint Formula

 

 

 

 

 

 

 

 

To find a missing endpoint:

 

 

 

 

 

 


 

Section 1.4 Angle Measure

 

 

 

 

 

Angle—consists of two noncollinear rays with the same endpoint.

Sides of an angle—the rays that form the angle.

Vertex of an angle—the initial point of each ray.

The measure of an angle (m<A) is equal to a number of degrees measured with a protractor.

 

 

 

 

 

An angle is named using points on the angle.

example: 

 

   

Interior of an Angle—all points between the sides of the angle.

Exterior of an Angle—all points not on or in the interior of the angle.

On an Angle--means the point lies on one of the sides of the angle.

 

Classification of Angles

Acute—measure of between 0 and 90 degrees

Right—measure of exactly 90 degrees

Obtuse—measure of between 90 and 180 degrees

 

Congruent Angles--angles with exactly the same measure.

Angle Bisector--a ray that divides an angle into two congruent angles.

 

 

Section 1.5 Angle Relationships

 Adjacent Angles—share a vertex and one side with no common interior points.

 Vertical Angles--two nonadjacent angles formed by intersecting lines.  These are always congruent.

 

Linear pairs--two adjacent angles whose non-shared sides form a line.  These always have a sum of 180 degrees.

Complementary angles—two angles whose sum is 90 degrees. (they do not need to be adjacent angles, but they can be.)

  

Note that these two angles can be "pasted" together to form a right angle!

 

Supplementary angles—two angles whose sum is 180 degrees.  (they do not need to be adjacent angles, but they can be.)

These two angles are supplementary.

 

Note that these two angles can be "pasted" together to form a straight line!

 

Perpendicular Lines--Lines that intersect to form right angles.

The symbol for perpendicular is: 

example:  says that line AB is perpendicular to line XY

 

Section 1.6 Polygons

Polygon--a closed figure whose sides (at least 3) are segments that intersect only at their endpoints.

 Polygon examples: 

 

Nonpolygon examples:

NAMING POLYGONS

Number of Sides

Name of Polygon

3

Triangle

4

Quadrilateral

5

Pentagon

6

Hexagon

7

Heptagon

8

Octagon

9

Nonagon

10

Decagon

12

Dodecagon

n

n-gon

 

Convex Polygon—no line that contains a side contains any interior points.  

 

Concave Polygon—a polygon that is not convex.  

 

Regular Polygon--all sides and angles are congruent.

 

Perimeter of a Polygon--the sum of the lengths of all sides.

The perimeter of this rectangle is ______