1. Points, Lines, and Planes The Three Undefined Terms of Geometry
2. A point is an exact location in space. You are here.
3. A true point has no length, no width, and no height. In fact, you cannot see a true point.
4. A point is named by a letter. P Point P
5. Lines are 1-dimensional objects that have only length. Lines continue forever in both directions.
6. Because a line has no width or height, you cannot see a true line.
7. A line is defined by 2 points. A B Line AB
8. A plane is a flat surface that has length & width but no height.
9. You can see a plane only if you view it at a certain angle.
10. A true plane goes on forever in all directions.
11. A true plane goes on forever in all directions.
12. A true plane goes on forever in all directions.
13. A true plane goes on forever in all directions.
14. A true plane goes on forever in all directions.
15. Planes can…
16. Planes can intersect.
17. An X-Wing fighter from Star Wars has wings that intersect.
18. Planes can be perpendicular.
19. Planes can be parallel.
20. A Tie Fighter from Star Wars has wings that are parallel.
21. Planes can be… intersecting perpendicular parallel
22. A ray has a starting point but no ending point.
23. A ray of light has a starting point (like the sun) and continues forever in the same direction.
24. Of course, if the ray hits an object, the light could be absorbed or reflected. MIRROR
25. A ray is also defined by 2 points. C D Ray CD
26. Def : Rays Geometry Lesson: Rays, Angles A ray is a part of a line that consists of an endpoint, and all points on one side of the endpoint. Def: Opposite Rays Opposite Rays are two rays of the same line with a common endpoint and no other points in common. P A A B P
27. A line segment has a starting point and an ending point. Line segments can be measured.
28. A line segment also defined by 2 points. E F Line Segment EF
29. Lines can do various things .
30. Lines can intersect at a point to form angles. X Y Z
31. Angles are defined by 3 points. X Z Y XYZ
32. Def :Angle: Geometry Lesson: Rays, Angles An angle is the union of two rays having the same endpoint. Three capital letters, with vertex in the middle : Single lowercase letter or number inside the angle: Use the name of the vertex angle if it’s the only angle at that vertex: side side vertex B A C x Naming Angles: a) b) c)
33. These angles can be right angles. 90
34. When lines intersect to form right angles, they are said to be perpendicular. V R T U c S UT RV
35. These angles can be right angles. c R S T U V RST = 90 ⁰ USR = 90 ⁰ USV = 90 ⁰ TSV = 90 ⁰
36. Lines can also run into each other to form straight angles.
37. Def: Straight Angle Geometry Lesson: Rays, Angles A straight angle is the union of two opposite rays. A B O Straight angles have a measure of 180 ° Def : Righ t Angle: M Q P A right angle has a measure of 90 °
38. 180 is a straight angle
39. Lines can intersect to form acute and obtuse angles. 135 obtuse 45 acute
40. Def: Acute Angle: Geometry Lesson: Rays, Angles Y X Z An acute angle has a measure greater than 0 ° and less than 90 °. Def: Obtuse Angle: Q X R An obtuse angle has a measure greater than 90 ° and less than 180°.
41. Angle Measure: Geometry Lesson: Rays, Angles Def: Congruent Angles B A C 25 ° are angles having equal measure. Ans. The measure of an angle is the number of degrees in the angle. Q: Which of the following angles are congruent? A) 45 ° A C) C 45 ° B) B 45 °
42. Def: Perpendicular Lines Geometry Lesson: Rays, Angles are two lines that intersect to form right angles . Right Angles: Straight Angle: Are lines m and l perpendicular? NOT UNLESS SPECIFIED BY THE GIVEN INFO OR A BOX IN THE DIAGRAM !!!! l m H K L J
43. Lines do not always intersect.
44. Lines can be parallel.
45. Parallel lines have the same slope or steepness.
46. Is it possible for lines not to intersect and not be parallel either?
47. Believe it or not, this is possible. Let’s consider a 3-dimensional rectangular prism.
48. These 2 lines are not parallel, but they are not intersecting either.
49. These lines are called skew lines.
50. You might have heard the word “skewer” the last time you had a barbecue. S K E W E R
51. A skewer raises your “dinner” off the surface of the grill. The skewer does not intersect the grill, and the skewer is not parallel to the grill.
52. Lines can be… intersecting perpendicular 90 º parallel skew