Download Lesson 1_1

Lesson 1.1 Notes
A definition is a statement that explains/clarifies the meaning of a word or phrase.
It is impossible to define point, line, and plane without using other words that need to
be defined. For this reason, these terms remain undefined. Using these three
undefined terms, you can define all other geometric figures and terms.
Point: represented on paper as a small dot, however, a point has no size, thickness, or
width. It is the smallest figure in geometry and it shows a location. It is the most basic
building block of geometry. In a two-dimensional coordinate system, a point’s
location is represented by an ordered pair of numbers (x, y). You name it with a
capital letter.
Point A
Point B
Line: a series of adjacent points that extend indefinitely. (In two opposite directions)
It is a straight path that has length but no width or thickness and goes on forever. It
has arrows on both sides. It is one dimensional. Any two points on a line name or
define it.
Plane: a collection of points lying on a flat surface that extends indefinitely in all
directions. It has length and width but no thickness and goes forever. It extends
infinitely along its edges. So it is two dimensional. Three Non-collinear points define a
plane. You also name a plane with a script capital letter such as P.
Line Segment: is a portion of a line between two points, called the endpoints.
Ray: is a part of a line that consists of an initial point and all points in the line.
Opposite rays are two rays that have common endpoint and form a line. It has two
arrows. It has one endpoint.
Angle: is a figure that is formed from two rays that extend from a common point
called the vertex.
Angle B is the name of the angle
Angle ABC is also the name of the
angle
Angle B is the vertex
The symbol m ∠ is used to denote the measure of an angle.
The unit of measure for angles is in degrees.
There are 360 degrees around a circle.
When two angles have the same measure, the angles are congruent. See
below for symbols.
Supplementary Angles are two angles whose sum measure 180 degrees.
Complementary Angles are two angles whose sum measure 90 degrees.
Vertical angles are angles whose sides form two pairs of opposite rays with
the same initial point. Vertical angles are congruent. The plural of vertex
(initial point) is vertices.
Linear pair: two adjacent angles that measure 180 degrees.
Collinear means on the same line: A set of points that lie in a straight line
Non-collinear points are points that do not lie on the same line. Look at points D, E,
and F.
Coplanar means on the same plane: A set of points, lines, line segments, rays or
any other geometrical shapes that lie on the same plane are said to be Coplanar.
Non-coplanar points are points that do not lie in the same plane. Look at point I.
Postulate or axiom is a statement that is accepted as true without proof.
Distance is the absolute value of the difference of the between coordinates.
Length is the distance measured between any two points.
Tick marks are used to show equal (congruent) segments. The figure shows three
marks to show three equal segments.
Congruence:
Midpoint is the middle point of a segment that divides a segment equally.
The point M of AB where AM = AB
Bisect means divide or cut in two equal parts. The diagrams show a line bisecting a
line segment, AB. and a ray bisecting an angle into equal angles.
Segment bisector: Any ray, segment, or line that intersects a segment at its midpoint.
The point M is the midpoint. The lines cut into two equal segments.
Examples:
Name each line in two different ways.
Name each midpoint and the segment it bisects.
Name the ray in two different ways.
Lesson 1.2 Notes:
An angle is formed by two rays that share a common endpoint, provided that the
two rays are non-collinear. In other words, the rays cannot lie on the same line.
The common endpoint of the two rays is the vertex of the angle. The two rays are
the sides of the angle.
The measure of an angle is the smallest amount of rotation about the vertex
from one ray to the other, measured in degrees. According to this definition, the
measure of an angle can be any value between 0° and 180°. The largest amount of
rotation less than 360° between the two rays is called the reflex measure of an
angle.
How to use a protractor:
Lesson 1.3
Remember what a definition is???
When you compare and contrast two figures, you describe how they are alike or
different. (Similarities and Differences)
Once you’ve written a definition, you should test it. To do this, you look for a
counterexample. That is, try to create a figure that fits your definition but isn’t
what you’re trying to define. If you can come up with a counterexample for your
definition, you don’t have a good definition.
Everyone knows, “A square is a figure with four equal sides.” What’s wrong with
this definition?
One better definition is: “A square is a 4-sided figure that has all sides congruent
and all angles measuring 90 degrees.”