1. Foundations of Geometry
Unit 1 Lesson 1 Notes
Foundations of Geometry

2. 1-1 Point - a location that has no size.
Line - an infinite number of points on a straight path that extends in two opposite directions with no end and has no thickness.
Plane - is an infinite number of points and lines on a flat surface that extends without end and has no thickness.
Segment - a part of a line with two endpoints and contains all points between them. P
A B l A B C A C B

3. 1-1
Ray - a part of a line that has one end point but continues forever in one direction and contains all the points in that direction.
Opposite rays - two rays that share one endpoint on the same line.
Angle - this or formed by two rays that share an endpoint. Each ray forms the side of an angle while the shared endpoint is the vertex. C D S T U P Q R

4. Does not need to be copied will be discussed and reviewed. 1-1
Postulate – a statement that is assumes to be true.
Collinear Points – points on the same line.
Distance on a line – the distance between any two points X and Y is the absolute value of the difference of their coordinates.
Construction – a geometric figure made with a compass and or a straight edge.
Congruent Segments – Segments that have the same length.
Congruent Angles – Angles with the same measure.

5. Postulates 1-1 Postulate 1-1 : Ruler Postulate
Every point on a line can be paired with a unique real number. This number is called the coordinate of the point.
Postulate 1-2 : Segment Addition Postulate
If points A, B, and C are on the same line, with B between A and C, then AB + BC = AC.
Postulate 1-3 : Protractor Postulate
Given Ray BA and a point C not on ray BA, a unique real number from 0 to 180 can be assigned to BC. 0 is BA and 180 is BD.
Postulate 1-4 : Angle Addition Postulate
If point D is in the interior of angle ABC the m< ABD + m< DBC = m< ABC