1. Introduction to Geometry – Points, Lines, and Planes Points - have no height or width - represented using a dot and labeled using a capital letter A B C D

2. Introduction to Geometry – Points, Lines, and Planes Points - have no height or width - represented using a dot and labeled using a capital letter A B C D Line - has no thickness. Its only dimension is length. - has no endpoints. It extends forever in each direction. ( arrows ) - it is ALWAYS straight - labeled with a lower case script letter ( line a ) - if there are points on the line, you can also name it using the points. ( line AB ) - the part of the line between A and B is called a line segment - line segments have definite endpoints a A B A B

3. Introduction to Geometry – Points, Lines, and Planes Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear A B C

4. Introduction to Geometry – Points, Lines, and Planes Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear A B C D E F

5. Introduction to Geometry – Points, Lines, and Planes Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear A B C D E F

6. Introduction to Geometry – Points, Lines, and Planes Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear A B C D E F

7. Introduction to Geometry – Points, Lines, and Planes Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear A B C D E F Ray – starts at a fixed point and continues in one direction forever

8. Introduction to Geometry – Points, Lines, and Planes Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear A B C D E F Ray - starts at a fixed point and continues in one direction forever - named from their starting point and one other point on the ray ( ray AC or ) A C

9. Introduction to Geometry – Points, Lines, and Planes Collinear - points that are on the SAME line - a line is really a collection of points - points A, B, and C are collinear - points D, E, and F are also collinear - points A and F are non-collinear - points B, E, and F are non-collinear A B C D E F Ray - starts at a fixed point and continues in one direction forever - named from their starting point and one other point on the ray ( ray AC or ) - two rays connected at the same starting point create an angle A C

10. Introduction to Geometry – Points, Lines, and Planes Geometric plane – a flat surface that has height and width. No thickness.

11. Introduction to Geometry – Points, Lines, and Planes Geometric plane - a flat surface that has height and width. No thickness. - it is two – dimensional and extends in all directions into infinity - named with capital script letters ( plane K ) K

12. Introduction to Geometry – Points, Lines, and Planes Geometric plane - a flat surface that has height and width. No thickness. - it is two – dimensional and extends in all directions into infinity - named with capital script letters ( plane K ) - also can be named using three points NOT on the same line ( plane DEF ) D E F

13. Introduction to Geometry – Points, Lines, and Planes Geometric plane - a flat surface that has height and width. No thickness. - it is two – dimensional and extends in all directions into infinity - named with capital script letters ( plane K ) - also can be named using three points NOT on the same line ( plane DEF ) D E F K C B A H I Points lie on planes and are in planes.

14. Introduction to Geometry – Points, Lines, and Planes Geometric plane - a flat surface that has height and width. No thickness. - it is two – dimensional and extends in all directions into infinity - named with capital script letters ( plane K ) - also can be named using three points NOT on the same line ( plane DEF ) D E F K C B A H I Points lie on planes and are in planes. Lines contain points and are in planes

15. Introduction to Geometry – Points, Lines, and Planes Geometric plane - a flat surface that has height and width. No thickness. - it is two – dimensional and extends in all directions into infinity - named with capital script letters ( plane K ) - also can be named using three points NOT on the same line ( plane DEF ) D E F K C B A H I Points lie on planes and are in planes. Lines contain points and are in planes Planes contain points and lines

16. Introduction to Geometry – Points, Lines, and Planes Planes exist in three – dimensional space and contain their own points and lines. In geometry, you can have multiple planes. ( Planes A and B ) A C B E D F A B

17. Introduction to Geometry – Points, Lines, and Planes Planes exist in three – dimensional space and contain their own points and lines. In geometry, you can have multiple planes. ( Planes A and B ) Line AB is in plane A but not in plane B. A C B E D F A B

18. Introduction to Geometry – Points, Lines, and Planes Planes exist in three – dimensional space and contain their own points and lines. In geometry, you can have multiple planes. ( Planes A and B ) Line AB is in plane A but not in plane B. Point F is in plane B but not in plane A. A C B E D F A B

19. Introduction to Geometry – Points, Lines, and Planes Planes exist in three – dimensional space and contain their own points and lines. In geometry, you can have multiple planes. ( Planes A and B ) Line AB is in plane A but not in plane B. Point F is in plane B but not in plane A. Points or lines that lie in the same plane are called coplanar A C B E D F A B

20. Introduction to Geometry – Points, Lines, and Planes Here is an example of points and lines that DO NOT lie in plane A. A C B E D F A

21. Introduction to Geometry – Points, Lines, and Planes Here is an example of points and lines that DO NOT lie in plane A. Points F, D and E are not in plane A. A B E D F A C

22. Introduction to Geometry – Points, Lines, and Planes Here is an example of points and lines that DO NOT lie in plane A. Points F, D and E are not in plane A. Line DE is not in plane A. A B E D F A C

23. Introduction to Geometry – Points, Lines, and Planes Here is an example of points and lines that DO NOT lie in plane A. Points F, D and E are not in plane A. Line DE is not in plane A. Lines intersect planes they are not contained in at exactly one point ( point C ) A B E D F A C

24. Introduction to Geometry – Points, Lines, and Planes Line Postulate – for any two points, there is exactly one line containing them. A B - a straight line is the shortest distance between two points.

25. Introduction to Geometry – Points, Lines, and Planes Line Postulate – for any two points, there is exactly one line containing them. A B - a straight line is the shortest distance between two points. Theorem – if two lines intersect, they intersect at exactly one point. E

26. Introduction to Geometry – Points, Lines, and Planes TermDimensionsMust Contain LineOne2 points PlaneTwo3 or more non collinear points SpaceThree4 or more noncoplanar points

27. Introduction To Geometry – Intersecting Lines and Planes In geometry you have : - lines intersecting lines

28. Introduction To Geometry – Intersecting Lines and Planes In geometry you have : - lines intersecting lines - planes intersecting planes - lines intersecting planes

29. Introduction To Geometry – Intersecting Lines and Planes Postulate – if two planes intersect, their intersection forms a line. Postulate – a line not contained in a plane will intersect that plane at exactly one point C

30. Introduction To Geometry – Intersecting Lines and Planes A line in a plane divides the plane into two half – planes. half – plane a

31. Introduction To Geometry – Intersecting Lines and Planes A line in a plane divides the plane into two half – planes. half – plane a Points A and B lie in the same half – plane. A B