Foundations of Geometry Unit 1 Lesson 1 Notes Foundations of Geometry

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

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

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.

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