•. Geometry is by far the. oldest branch of. mathematics. • • Geometry is by far the oldest branch of mathematics. • Every ancient civilization developed some form of geometry, as a way of helping with survival.

•. Geometry as we know it. today was first developed • Geometry as we know it today was first developed by Greeks who lived in what is now Egypt.

•. Geometry was formally. organized by the. mathematician Euclid in a • Geometry was formally organized by the mathematician Euclid in a book called The Elements around 300 B.C.

•. Every geometry book for. the past 2,300 years has • Every geometry book for the past 2,300 years has been based on Euclid’s Elements. 

Geometry •. literally means “earth. measure” • Geometry • literally means “earth measure” • study of shapes and their relationships

Main “building blocks” of geometry

•. point. •. a location, usually. represented by a dot. • • point • a location, usually represented by a dot • points are infinitely small • no length, width, or thickness • 0 dimensions

• We typically represent points with dots and name them with capital letters.

•. line. •. shortest path from one. point to another. • • line • shortest path from one point to another • infinitely thin; no thickness • extends forever in opposite directions • 1 dimension

• Usually named by two points that form it.

•. Lines are named with. TWO points (not 3 or. more). • • Lines are named with TWO points (not 3 or more) • You put a line symbol (double arrow) above the name of a line.

•. Lines can also be. named with small. cursive (or italic). letters • Lines can also be named with small cursive (or italic) letters. These are lines l and m .

Give as many names for this line as you can.

• plane

• plane

•. plane. •. flat surface with no. thickness and no. boundaries. • • plane • flat surface with no thickness and no boundaries • extends forever, but infinitely thin • 2 dimensions

•. We most often show. planes by drawing a. parallelogram (or other • We most often show planes by drawing a parallelogram (or other four-sided shapes)

• Planes are often names with capital, cursive letters.

•. You can also name a. plane with three points • You can also name a plane with three points that are on it, like ABC.

In most cases we will just consider single planes, but we can also talk about • space • all the possible points in 3 dimensions

Collinear on the same line Coplanar on the same plane

Parts of lines

•. Segment. •. Connects two points. •. Stops at the endpoints. • • Segment • Connects two points • Stops at the endpoints • Named by putting a bar above the endpoints

•. Ray. •. Extends endlessly in. one direction. • • Ray • Extends endlessly in one direction • Starts at an endpoint and continues.

•. Named with an. endpoint and one other. point on the ray, with • Named with an endpoint and one other point on the ray, with an arrow above them. (The first letter must be the endpoint.)

• Opposite rays • Share the same endpoint • Together make a line

Postulate . A statement that is so. obvious we assume it is Postulate  A statement that is so obvious we assume it is true without questioning it.

 We use postulates to explain why other things are true.

 Euclid built all of geometry from just 5 postulates.  We’ll use a lot more, 4 of which we’ll learn today.

 Through any 2 points there is exactly 1 line.

 If 2 lines intersect, the intersection is a point.

 Through any 3 noncollinear points there is exactly 1 plane.

 If 2 planes intersect, the intersection is a line.

Know … . History of geometry . Point, line, plane, space  Know …  History of geometry  Point, line, plane, space  Collinear, coplanar  Segment, ray, opposite rays  Postulate  4 basic postulates of points, lines, & planes