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# Pointslinesplanesrays, segments and parallel, perpendicular and skew

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### Transcript

• 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 &amp; 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
• 53. The end.