The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are.

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Presentation transcript:

The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.

Undefined Terms POINT point A LINE 1 MN PLANE 2 plane DEF Dimensions Representation Name POINT point A A LINE 1 MN M N PLANE D E 2 plane DEF F Lines – any 2 points define a line. Planes – any 3 non-collinear points define a plane.

Point: A Point is named by a capital letter and represented by a dot. Properties Point: A Point is named by a capital letter and represented by a dot. A point names a location and has no size J Called Point J All geometric figures are comprised of points.

Properties A line has no thickness or width. It is an infinite set of points (extends forever). A line is named by 2 points on the line and by placing the line symbol above the letters.

Properties Plane A flat surface that extends indefinitely in all directions (consists of an infinite set of points) Named by 3 points not on the same line or a capital letter.

Practice with a partner Look around the classroom. Name 3 points Name 2 lines Name one plane

Defined Terms SEGMENT RAY OPPOSITE RAYS Term Representation Name AB CD FE and FG E F G

Definitions Segment – a part of a line with two endpoints and all the points between them. Ray – a part of a line with one endpoint that goes infinitely in one direction. Opposite Rays – a pair of rays that 1) share the same endpoint 2) together form a line.

Practice with a partner Look around the room at all the points How can you use these points to create: A segment A Ray Opposite rays

A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

Intersections The intersection of two lines is a POINT. The intersection of two planes is a LINE. The intersection of a plane and a line is a POINT.

1.3 Measuring Segments Ruler Postulate Every point on a line can be paired with a real number. The real number that corresponds to the point is called the coordinate of the point. The distance between any two points is the absolute value of the difference of the corresponding numbers (on a number line or ruler)

Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC C B A

Example If DT = 60, find the value of x. Then find DS and ST. 2x - 8

Congruent vs. Equal

Midpoint Midpoint: a point that divides the segment into two congruent segments B is the midpoint, so AB = BC A B C

Example C is the midpoint of AB. Find AC, CB, and AB. 2x + 1 3x – 4 A