Geometric Basics

Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the same letter in the same sketch. A B A

Lines B C n A Extend indefinitely and have no thickness or width. How to sketch : using arrows at both ends. How to name: 2 ways (1) small script letter line n (2) any two points on the line Never name a line using three points n A B C

Collinear Points Lie on the same line. (The line does not have to be visible). A B C Non collinear C A Collinear B

Planes Flat surface that extends indefinitely in all directions. How to sketch: Use a parallelogram (four sided figure) How to name: 2 ways (1) Capital script letter Plane M (2) Any 3 non collinear points in the plane Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C Horizontal Plane Vertical Plane Other

Different planes in a figure: B Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc. D C E F H G

Other planes in the same figure: Any three non collinear points determine a plane! Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc.

Coplanar Objects Coplanar objects (points, lines, etc.) lie on the same plane. The plane does not have to be visible. Are the following points coplanar? A, B, C ? Yes A, B, C, F ? No H, G, F, E ? Yes E, H, C, B ? Yes A, G, F ? Yes C, B, F, H ? No

Segment Definition: Part of a line that consists of two points called the endpoints and all points between them. How to sketch: How to name: AB (without a symbol) means the length of the segment or the distance between points A and B.

Congruent Segments Congruent segments can be marked with dashes. Definition: Segments with equal lengths. (congruent symbol: ) Congruent segments can be marked with dashes.

Ray Definition: RA : RA and all points Y such that A is between R and Y. How to sketch: How to name: ( the symbol RA is read as “ray RA” )

Opposite Rays Definition: If A is between X and Y, AX and AY are opposite rays. ( Opposite rays must have the same “endpoint” ) opposite rays not opposite rays

Intersection of Figures The intersection of two figures is the set of points that are common in both figures. The intersection of two lines is a point. m P n Line m and line n intersect at point P.

3 Possibilities of Intersection of a Line and a Plane (1) Line passes through plane – intersection is a point. (2) Line lies on the plane - intersection is a line. (3) Line is parallel to the plane - no common points.

Intersection of Two Planes is a Line. B P A R Plane P and Plane R intersect at the line

Segment Bisectors Definition: Any segment, line or plane that divides a segment into two congruent parts is called segment bisector.

Between AX + XB = AB AX + XB > AB Definition: X is between A and B if AX + XB = AB. AX + XB = AB AX + XB > AB

The Segment Addition Postulate If C is between A and B, then AC + CB = AB. Example: If AC = x , CB = 2x and AB = 12, then, find x, AC and CB. 2x x 12 Step 1: Draw a figure Step 2: Label fig. with given info. AC + CB = AB x + 2x = 12 3x = 12 x = 4 Step 3: Write an equation x = 4 AC = 4 CB = 8 Step 4: Solve and find all the answers

You Try It! Complete Practice Problems and check your answers with one another.