1. Chapter Introductory Geometry 11 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

2. 11-1 Basic Notions  Linear Notions  Planar Notions  Other Planar Notions  Angles  Angle Measurement  Types of Angles  Perpendicular Lines  A Line Perpendicular to a Plane Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

3. Undefined terms: points, lines, and planes Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

4. Lines A line has no thickness and it extends forever in two directions. Given two points, there is one and only one line that connects these points. If P and Q are any two points, we can create a number line on the line PQ such that there is one- to-one correspondence between the points on the line and real numbers. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

5. Linear Notions Collinear points  Line ℓ contains points A, B, and C.  Points A, B, and C belong to line ℓ.  Points A, B, and C are collinear.  Points A, B, and D are not collinear. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

6. Between  Point B is between points A and C on line ℓ.  Point D is not between points A and C. Linear Notions Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

7. Line segment A subset of a line that contains two points of the line and all points between those two points. Linear Notions AB or BA Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

8. Ray A subset of the line AB that contains the endpoint A, the point B, all points between A and B, and all points C on the line such that B is between A and C. Linear Notions AB Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

9. Planar Notions Coplanar  Points D, E, and G are coplanar.  Points D, E, F, and G are not coplanar.  Lines DE, DF, and FE are coplanar.  Lines DE and EG are coplanar.  Lines DE and EG are intersecting lines; they intersect at point E. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

10. Skew lines  Lines GF and DE are skew lines. They do not intersect, and there is no plane that contains them. Concurrent lines  Lines DE, EG, and EF are concurrent lines; they intersect at point E. Planar Notions Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

11. Parallel lines Line m is parallel to line n. They have no points in common. Planar Notions Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

12. Axioms About Points, Lines, and Planes  There is exactly one line that contains any two distinct points.  If two points lie in a plane, then the line containing the points lies in the plane.  If two distinct planes intersect, then their intersection is a line.  There is exactly one plane that contains any three distinct noncollinear points. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

13. Theorems About Points, Lines, and Planes  A line and a point not on the line determine a plane.  Two parallel lines determine a plane.  Two intersecting lines determine a plane. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

14. Other Planar Notions Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

15. Half plane Line AB separates plane  into two half- planes. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

16. Angles Angle – formed by two rays with the same endpoint. Sides of an angle – the two rays that form an angle. Vertex – the common endpoint of the two rays that form an angle. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

17. Angles Adjacent angles – two angles with a common vertex and a common side, but without overlapping interiors.  QPR is adjacent to  RPS. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

18. Angle Measurement Protractor Degree : of a rotation about a point Second : of a minute Minute : of a degree Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

19. Example 11-1 a.Find the measure of  BAC if m  1 = 47°45′ and m  2 = 29°58′. b.Express 47°45′36″ as a number of degrees. m  BAC = 17°47′ 47°45′36″ = 47°+ 0.75° + 0.01° = 47.76° Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

20. Types of Angles Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

21. Types of Angles Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

22. Perpendicular Lines Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

23. A Line Perpendicular to a Plane A line perpendicular to a plane is a line that is perpendicular to every line in the plane through its intersection with the plane. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

24. Perpendicular Planes If P is any point on AD, Q in plane α, and S in plane β so that PQ  AD and PS  AD, then  QPS is also a right angle. Since  QPS measures 90°, the planes are perpendicular. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

25. Dihedral Angles A dihedral angle is formed by the union of two half-planes and the common line defining the half-planes. A dihedral angle is measured by any of the associated planar angles such  OPD, where PO  AC and PD  AC. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.