The document covers fundamental concepts in geometry including points, lines, planes, angles, and postulates. It provides definitions, examples, and problems related to conjectures, collinear points, parallel lines, and various types of angles. Additionally, it includes homework assignments and quizzes to reinforce understanding of these geometric principles.

1. Points, Lines, Planes1-3

2. Quiz What is a conjecture?Give a counterexample: The product of 2 positive numbers is greater than either number.Use inductive reasoning: 2, 6, 7, 21, 22, 66 67, ….Make a conjecture about the sum of the first 500 positive even numbers.

3. Collinear and Noncollinear PointsPoints that are on the same line are called collinear points.If a single line cannot be drawn through all the points, then the points are noncollinear.WUEFCDXVCollinear pointsNoncollinear points

4. Collinear PointsAre points E, F, and C collinear?Can you label line m in three ways?Are points E, F, and D collinear?Are points F, P, and C collinear?nmCEFPDl

5. PlanesIntersecting lines are lines that cross (intersect) at exactly one point.Parallel lines are lines that do not cross They have no points in common.Skew lines are not parallel and they do not intersect. They lie in different planes.

6. PlanesList three different names for the plane represented by the top of the box.GHFECAB

7. Basic Postulates of GeometryPostulate 1-1: Through any two points there is exactly one line.

8. Basic Postulates of GeometryPostulate 1-2If two lines intersect, then they intersect in exactly one point.

9. Basic Postulates of GeometryPostulate 1-3If two planes intersect, then they intersect in exactly one line.RSWT

10. Basic Postulates of GeometryPostulates1-4Through any three noncollinear points there is exactly one plane.

11. Homework Prentice Hall GeometryPage 19- 20 # 2- 32 even16 problems

12. Angles

13. QUIZ What is the answer to number…..6814202830

14. SegmentsA segment is a part of a line with two endpoints.RBRead it as: “Segment RB” or “Segment BR”Write it as:RBorBR

15. RaysA ray consists of an endpoint and all the points of a line on one side of the endpoint.CDRead it as: “Ray CD” (the order does matter)Write it as:CD

16. VocabularyAn angle has two sides and a vertex.The sides of the angles are rays. The rays share a common endpoint (the vertex)Angles are measured in units called degrees.

17. Right AnglesForms a square cornerForms a 90 degree angle.90 degrees

18. Straight AngleForms a straight lineAngle is 180 degrees180 degrees

19. Types of AnglesWhen lines intersect to form right angles, then they are classified as perpendicular lines.

20. What do we use to help us?A protractorHere is a standard protractor like you use in the classroom.

21. When we use a protractor, we need to line it up correctly.You need to make sure the protractor is lined up correctly.Is this ready to measure the angle?

22. Were you right.................it wasn’tLook for the upside down ‘T’ in the middle of the straight line on your protractor. This needs to be exactly on the vertex of your angle.

23. We need to remember.....It doesn’t matter which way round the angle is, you ALWAYS need to line the upsidedown ‘T’ to the vertexof the angle.

24. Now you are ready.Read from the 0°, and follow the inner set of numbers.

25. Homework Page 25# 1-15 Homework Prentice Hall Geometry

26. QUIZ 1. When two lines are skew, it means three things. What are those three things? 2. Demonstrate how to label a line, plane, ray, and segment.3. An angle is made up of two ____ sharing a common point called _____.

27. 4. The term skew is a Middle English word meaning "to escape." Skew lines cannot be contained in one plane. Therefore, they have "escaped" a plane. What is something in your life that you have skewed from, for the better?

28. Labeling AnglesMust have three points. One on each ray and the vertex.BLabeled as: ∠ BCD or ∠DCBCD

29. Complementary AnglesIf the sum of the measures of two angles is exactly 90º then the angles are complementary.

30. Supplementary AnglesIf the sum of the measures of two angles is exactly 180º then the angles are supplementary.

31. Vertical AnglesTwo angles whose sides are opposite rays.

32. Vertical AnglesVertical angles are congruentCongruent means same or equal.In this picture, <1 and <3 are vertical angles.What is the measure of <2?<2 is 120º because it is congruent to the vertical angle across from it.

33. Adjacent AnglesTwo coplanar angles with a common side, a common vertex, and no common interior points.∠ABC is adjacent to ∠CBDACBD

34. Review! Name each picture.

35. Postulates. Angle Addition PostulateIf point B is in the interior of ∠AOC, then m ∠AOB + m ∠BOC = m ∠AOC.ABOC

36. Postulates.Angle Addition PostulateIf ∠AOC is a straight angle, then m ∠AOB + m ∠BOC = 180.BAOC

37. Homework Prentice Hall Geometry