Points, Lines, and Planes Three Dimensional Geometry

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Presentation transcript:

Points, Lines, and Planes Three Dimensional Geometry But not airplanes!

Undefined Terms Point: Has no dimension, in other words no length, width, or thickness named by a single letter Line: has no thickness but its length extends in one dimension and goes on forever in both directions. Name by two points on the line or by a single lowercase letter •A A B r

Planes Planes have no thickness but extend indefinitely in all directions. Represented by a shape that resembles a tabletop or parallelogram Planes are named by: A single letter Example: plane m Any three points in the plane Example: Plane ABC

Important Vocabulary Collinear points Points on the same line A• B• c• Non – collinear points Points not on the same line A• B• C• Coplanar points A set of all points lying in the same plane A• B• C•

Important Vocabulary Coplanar Lines Lines that lie in the same plane Skew Lines Lines that do no lie in the same plane

Skew Lines Skew lines Lines that are not parallel or intersecting D F H Note: NO plane will contain lines AB and CD. C E G A B

Lines and Planes A line can be in a given plane OR A line can intersect a plane at one point A line may not intersect a plane at all and is parallel to the plane N • p N N

What Determines a Plane? Three noncollinear points A line and a point not on the line • • • • • •

What Determines a Plane? Two intersecting lines Two parallel lines

You’ve heard of parallel lines… What about parallel planes? Parallel Planes: Planes that do not intersect Are there parallel planes in the classroom?? YES!! The ceiling and floor Draw two parallel planes, call them j and k: k j

Intersecting Planes Use the picture to answer the following: What is formed when two planes intersect? Answer: A line Plane q and plane l intersect to form line AB

Intersecting Planes Dihedral Angle: the angle formed when two planes meet Naming Dihedral Angles A point in one plane – the edge – A point in the other plane Name at least two dihedral angles from the picture: F H Z R Dihedral angle F – CD – R Dihedral angle C – AB - H

Regents Questions 1. 2. 3 3

Regents Questions 3. 4

Practice with lines and planes 1. In this rectangular sided box, which set of sides lie in the same plane? Answer: AB and BC 2. True or false: When two planes intersect, two lines are formed. Answer: FALSE, only one line is formed.

Practice with lines and planes 3. Which of the following statements is TRUE from the picture? Answer: Point p is in plane l 4. If two lines intersect, only one plane contains both the lines. TRUE or FALSE? Answer: TRUE

Practice with lines and planes 5. For this rectangular solid, plane GHB and EFC are _____. Answer: Parallel 6. Which of the following statements is true from the picture? Answer: Plane l is perpendicular to line BC.

Practice with lines and planes 7. If two points lie in a plane, the line joining them also lies in the same plane. TRUE or FALSE? Answer: TRUE • • 8. For this rectangular solid, which plane(s) contain D and are parallel to plane FEG? Answer: Only plane DAB