Chapter 1 notes
Point—a single location in space, has no dimension,
usually represented by a small dot and named with a single capital letter.
Line
named
Collinear Points
Plane
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.
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)
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:
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
Vertical Angles
Linear pairs
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.
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 ______