Applied Geometry Lesson 1 2 Points Lines and

  • Slides: 13
Download presentation
Applied Geometry Lesson 1 -2 Points, Lines, and Planes Objective: Learn to identify and

Applied Geometry Lesson 1 -2 Points, Lines, and Planes Objective: Learn to identify and draw models of points, lines, and planes, and determine their characteristics.

Point – the basic unit of geometry l Has no size l Named using

Point – the basic unit of geometry l Has no size l Named using CAPITAL Letters l Read as point A

Line – a series of points that extends without end in two directions. Made

Line – a series of points that extends without end in two directions. Made up of an infinite number of points Arrows show that the line extends without end in both directions Named: either a single lowercase script letter OR 2 points on the line Named: line l or

Example 1 Name two points on line m point P and point Q (or

Example 1 Name two points on line m point P and point Q (or Point R) Give 3 names for the line

Definitions Collinear – points that lie on the same line Noncollinear – points that

Definitions Collinear – points that lie on the same line Noncollinear – points that do not lie on the same line.

Example 3 Name three points that are collinear and three points that are noncollinear.

Example 3 Name three points that are collinear and three points that are noncollinear. Collinear – A, B, E or D, B, C Must have commas! Noncollinear – A, B, D or C, B, E or A, B, C or D, B, E Otherwise you are naming a plane.

Ray – has a definite starting point and extends without end in one direction.

Ray – has a definite starting point and extends without end in one direction. The starting point of a ray is called the endpoint. A ray is named using the endpoint first, then another point on the ray. *Naming a ray: arrow always points right!

Ray cont… Look at the pairs of rays

Ray cont… Look at the pairs of rays

Line Segment – a part of a line consisting of 2 endpoints and all

Line Segment – a part of a line consisting of 2 endpoints and all points between Name using its endpoints

Example Name 2 segments and one ray. Sample answers: Don’t name the same thing

Example Name 2 segments and one ray. Sample answers: Don’t name the same thing twice unless it asked for the different ways of naming. Why does ray BD not work?

Plane – a flat surface that extends without end in all directions For any

Plane – a flat surface that extends without end in all directions For any 3 noncollinear points, there is only one plane that contains all 3 points. A plane can be named with a single uppercase script letter or by three noncollinear points. Plane named: ABC or M

Definitions Coplanar – Points that lie in the same plane Noncoplanar – Points that

Definitions Coplanar – Points that lie in the same plane Noncoplanar – Points that do not lie in the same plane.

Hands-On Activity Place points B, C, D, E near the corners of a piece

Hands-On Activity Place points B, C, D, E near the corners of a piece of paper. Place point A in the middle of the paper Fold the paper so that point A is on the crease. Open the paper slightly. The two sections of the paper represent different planes. A, E, D l Name 3 points that are coplanar l Name 3 points that are noncoplanar D, A, C l Name a point that is in both planes A

GEOMETRY Angles and Parallel Lines Intersecting Lines LinesGEOMETRY Angles and Parallel Lines Intersecting Lines Lines
Lines and Angles Geometry PARALLEL LINES Two linesLines and Angles Geometry PARALLEL LINES Two lines
Projective Geometry Projective Geometry Projective Geometry Projective GeometryProjective Geometry Projective Geometry Projective Geometry Projective Geometry
Geometry Lesson 1 1 Points Lines and PlanesGeometry Lesson 1 1 Points Lines and Planes
Geometry Lesson 1 1 Points Lines and PlanesGeometry Lesson 1 1 Points Lines and Planes
Geometry Lesson 1 1 Points Lines and PlanesGeometry Lesson 1 1 Points Lines and Planes
Lesson 1 1 Points Lines and Planes GeometryLesson 1 1 Points Lines and Planes Geometry
Lesson 1 1 Points Lines Planes Points HowLesson 1 1 Points Lines Planes Points How
Angles and Parallel Lines Intersecting Lines Lines thatAngles and Parallel Lines Intersecting Lines Lines that
Parallel and Perpendicular Lines Parallel Lines Two linesParallel and Perpendicular Lines Parallel Lines Two lines
Geometry 3 1 Lines and Transversals Parallel LinesGeometry 3 1 Lines and Transversals Parallel Lines
Parallel Lines Transversals Geometry Parallel Lines and TransversalsParallel Lines Transversals Geometry Parallel Lines and Transversals