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Points, Lines, Planes<br />1-3<br />
Quiz	<br />What is a conjecture?<br />Give a counterexample: The product of 2 positive numbers is greater than either numb...
Collinear and Noncollinear Points<br />Points that are on the same line are called collinear points.<br />If a single line...
Collinear Points<br />Are points E, F, and C collinear?<br />Can you label line m in three ways?<br />Are points E, F, and...
Planes<br />Intersecting lines are lines that cross (intersect) at exactly one point.<br />Parallel lines are lines that d...
Planes<br />List three different names for the plane represented by the top of the box.<br />G<br />H<br />F<br />E<br />C...
Basic Postulates of Geometry<br />Postulate 1-1: <br />Through any two points there is exactly one line.<br />
Basic Postulates of Geometry<br />Postulate 1-2<br />If two lines intersect, then they intersect in exactly one point.<br />
Basic Postulates of Geometry<br />Postulate 1-3<br />If two planes intersect, <br />then they intersect in <br />exactly o...
Basic Postulates of Geometry<br />Postulates1-4<br />Through any three noncollinear points there is exactly one plane.<br />
Homework			Prentice Hall Geometry<br />Page 19- 20<br /> # 2- 32 even<br />16 problems<br />
Angles<br />
QUIZ	<br />What is the answer to number…..<br />6<br />8<br />14<br />20<br />28<br />30<br />
Segments<br />A segment is a part of a line with two endpoints.<br />R<br />B<br />Read it as: “Segment RB” or “Segment BR...
Rays<br />A ray consists of an endpoint and all the points of a line on one side of the endpoint.<br />C<br />D<br />Read ...
Vocabulary<br />An angle has two sides and a vertex.<br />The sides of the angles are rays. The rays share a common endpoi...
Right Angles<br />Forms a square corner<br />Forms a 90 degree angle.<br />90 degrees<br />
Straight Angle<br />Forms a straight line<br />Angle is 180 degrees<br />180 degrees<br />
Types of Angles<br />When lines intersect to form right angles, then they are classified as perpendicular lines.<br />
What do we use to help us?<br />A protractor<br />Here is a standard protractor like you <br />use in the classroom.<br />
When we use a protractor, we need to line it up correctly.<br />You need to make sure the protractor is lined up correctly...
Were you right.................it wasn’t<br />Look for the upside down ‘T’ in the middle of the straight line on your prot...
We need to remember.....<br />It doesn’t <br />matter which <br />way round the <br />angle is, you <br />ALWAYS need <br ...
Now you are ready.<br />Read from the 0°, and follow the inner set of numbers.<br />
Homework	<br />Page 25<br /># 1-15 <br />Homework			Prentice Hall Geometry<br />
QUIZ	<br />1. When two lines are skew, it means three things. What are those three things? <br />2.  Demonstrate how to la...
4. The term skew is a Middle English word meaning &quot;to escape.&quot; <br />Skew lines cannot be contained in one plane...
Labeling Angles<br />Must have three points. One on each ray and the vertex.<br />B<br />Labeled as: <br />∠ BCD or ∠DCB<b...
Complementary Angles<br />If the sum of the measures of two angles is exactly 90º then the angles are complementary.<br />
Supplementary Angles<br />If the sum of the measures of two angles is exactly 180º then the angles are supplementary.<br />
Vertical Angles<br />Two angles whose sides are opposite rays.<br />
Vertical Angles<br />Vertical angles are congruent<br />Congruent means same or equal.<br />In this picture, &lt;1 and &lt...
Adjacent Angles<br />Two coplanar angles with a common side, a common vertex, and no common interior points.<br />∠ABC is ...
Review!		Name each picture.<br />
Postulates.	<br />Angle Addition Postulate<br />If point B is in the interior of ∠AOC, <br />then  m ∠AOB + m ∠BOC = m ∠AO...
Postulates.<br />Angle Addition Postulate<br />If ∠AOC is a straight angle, <br />then  m ∠AOB + m ∠BOC = 180.<br />B<br /...
Homework			Prentice Hall Geometry<br />
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Angles

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Angles

  1. 1. Points, Lines, Planes<br />1-3<br />
  2. 2. Quiz <br />What is a conjecture?<br />Give a counterexample: The product of 2 positive numbers is greater than either number.<br />Use inductive reasoning: <br /> 2, 6, 7, 21, 22, 66 67, ….<br />Make a conjecture about the sum of the first 500 positive even numbers.<br />
  3. 3. Collinear and Noncollinear Points<br />Points that are on the same line are called collinear points.<br />If a single line cannot be drawn through all the points, then the points are noncollinear.<br />W<br />U<br />E<br />F<br />C<br />D<br />X<br />V<br />Collinear points<br />Noncollinear points<br />
  4. 4. Collinear Points<br />Are points E, F, and C collinear?<br />Can you label line m in three ways?<br />Are points E, F, and D collinear?<br />Are points F, P, and C collinear?<br />n<br />m<br />C<br />E<br />F<br />P<br />D<br />l<br />
  5. 5. Planes<br />Intersecting lines are lines that cross (intersect) at exactly one point.<br />Parallel lines are lines that do not cross They have no points in common.<br />Skew lines are not parallel and they do not intersect. They lie in different planes.<br />
  6. 6. Planes<br />List three different names for the plane represented by the top of the box.<br />G<br />H<br />F<br />E<br />C<br />A<br />B<br />
  7. 7. Basic Postulates of Geometry<br />Postulate 1-1: <br />Through any two points there is exactly one line.<br />
  8. 8. Basic Postulates of Geometry<br />Postulate 1-2<br />If two lines intersect, then they intersect in exactly one point.<br />
  9. 9. Basic Postulates of Geometry<br />Postulate 1-3<br />If two planes intersect, <br />then they intersect in <br />exactly one line.<br />R<br />S<br />W<br />T<br />
  10. 10. Basic Postulates of Geometry<br />Postulates1-4<br />Through any three noncollinear points there is exactly one plane.<br />
  11. 11. Homework Prentice Hall Geometry<br />Page 19- 20<br /> # 2- 32 even<br />16 problems<br />
  12. 12. Angles<br />
  13. 13. QUIZ <br />What is the answer to number…..<br />6<br />8<br />14<br />20<br />28<br />30<br />
  14. 14. Segments<br />A segment is a part of a line with two endpoints.<br />R<br />B<br />Read it as: “Segment RB” or “Segment BR”<br />Write it as:<br />RB<br />or<br />BR<br />
  15. 15. Rays<br />A ray consists of an endpoint and all the points of a line on one side of the endpoint.<br />C<br />D<br />Read it as: “Ray CD” (the order does matter)<br />Write it as:<br />CD<br />
  16. 16. Vocabulary<br />An angle has two sides and a vertex.<br />The sides of the angles are rays. The rays share a common endpoint (the vertex)<br />Angles are measured in units called degrees.<br />
  17. 17. Right Angles<br />Forms a square corner<br />Forms a 90 degree angle.<br />90 degrees<br />
  18. 18. Straight Angle<br />Forms a straight line<br />Angle is 180 degrees<br />180 degrees<br />
  19. 19. Types of Angles<br />When lines intersect to form right angles, then they are classified as perpendicular lines.<br />
  20. 20. What do we use to help us?<br />A protractor<br />Here is a standard protractor like you <br />use in the classroom.<br />
  21. 21. When we use a protractor, we need to line it up correctly.<br />You need to make sure the protractor is lined up correctly.<br />Is this ready to measure the angle?<br />
  22. 22. Were you right.................it wasn’t<br />Look for the upside down ‘T’ in the middle of the straight line on your protractor. <br />This needs to be exactly on the vertex of your angle.<br />
  23. 23. We need to remember.....<br />It doesn’t <br />matter which <br />way round the <br />angle is, you <br />ALWAYS need <br />to line the upside<br />down ‘T’ to the vertex<br />of the angle.<br />
  24. 24. Now you are ready.<br />Read from the 0°, and follow the inner set of numbers.<br />
  25. 25. Homework <br />Page 25<br /># 1-15 <br />Homework Prentice Hall Geometry<br />
  26. 26. QUIZ <br />1. When two lines are skew, it means three things. What are those three things? <br />2. Demonstrate how to label a line, plane, ray, and segment.<br />3. An angle is made up of two ____ sharing a common point called _____.<br />
  27. 27. 4. The term skew is a Middle English word meaning &quot;to escape.&quot; <br />Skew lines cannot be contained in one plane. Therefore, they have &quot;escaped&quot; a plane. <br />What is something in your life that you have skewed from, <br />for the better?<br />
  28. 28. Labeling Angles<br />Must have three points. One on each ray and the vertex.<br />B<br />Labeled as: <br />∠ BCD or ∠DCB<br />C<br />D<br />
  29. 29. Complementary Angles<br />If the sum of the measures of two angles is exactly 90º then the angles are complementary.<br />
  30. 30. Supplementary Angles<br />If the sum of the measures of two angles is exactly 180º then the angles are supplementary.<br />
  31. 31. Vertical Angles<br />Two angles whose sides are opposite rays.<br />
  32. 32. Vertical Angles<br />Vertical angles are congruent<br />Congruent means same or equal.<br />In this picture, &lt;1 and &lt;3 are vertical angles.<br />What is the measure of &lt;2?<br />&lt;2 is 120º because it is congruent to the vertical angle across from it.<br />
  33. 33. Adjacent Angles<br />Two coplanar angles with a common side, a common vertex, and no common interior points.<br />∠ABC is adjacent to ∠CBD<br />A<br />C<br />B<br />D<br />
  34. 34. Review! Name each picture.<br />
  35. 35. Postulates. <br />Angle Addition Postulate<br />If point B is in the interior of ∠AOC, <br />then m ∠AOB + m ∠BOC = m ∠AOC.<br />A<br />B<br />O<br />C<br />
  36. 36. Postulates.<br />Angle Addition Postulate<br />If ∠AOC is a straight angle, <br />then m ∠AOB + m ∠BOC = 180.<br />B<br />A<br />O<br />C<br />
  37. 37. Homework Prentice Hall Geometry<br />

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