Planes, Lines and Transversals

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Planes, Lines and Transversals

  1. 1. PARALLEL LINES IN A PLANE<br />
  2. 2. ParallelandSkewLines<br />
  3. 3. pgs 77-78 <br />Parallel lines are coplanar lines that do not intersect.<br />AB || GH<br />Skew lines are non-coplanar lines which are neither parallel nor intersecting.<br />AB and HI are skew<br />Parallel planes are planes that do not intersect.<br />plane ABCD || plane GHIJ<br />Two segments and/or rays are parallel if and only if the lines containing them are also parallel.<br />AB || GH<br />
  4. 4. pg 78 <br />TRANSVERSALS<br />A line is a transversal if and only if it intersects two or more coplanar lines at different points.<br />referred to as “cutting” the lines<br />How many angles formed?<br />x<br />f<br />g<br />y<br />h<br />
  5. 5. pg 79 <br />Exterior<br />1<br />2<br />f<br />3<br />4<br />Interior<br />g<br />5<br />6<br />8<br />7<br />Exterior<br />h<br />Interior – region whose boundaries include the lines<br /> Exterior – region which has only one of the lines as its lone boundary<br />Interior angles: 3, 4, 5, 6<br />Exterior angles: 1, 2, 7, 8<br />
  6. 6. pg 80 <br />1<br />2<br />3<br />4<br />5<br />6<br />7<br />8<br />
  7. 7. EXAMPLE:<br />4<br />3<br />2<br />1<br />8<br />7<br />6<br />5<br />Give all the corresponding angles.<br /> 1 and 3 2 and 4<br /> 5 and 7 6 and 8<br />Give all the alternate interior angles.<br /> 2 and 7 3 and 6<br />3. Give all the alternate exterior angles.<br /> 1 and 8 4 and 5<br />
  8. 8. 4<br />5<br />9<br />6<br />3<br />2<br />7<br />8<br />Use the figure above and identify the following pairs (next slide) whether they are one of the following:<br />Corresponding angles<br />Alternate interior angles<br />Alternate exterior angles<br />Vertical angles<br />Linear pair<br />
  9. 9. Two angles are called vertical angles if and if only they are two nonadjacent angles formed by two intersecting lines.<br />Two angles form a linear pair if and only if the angles are adjacent and the non-common sides form opposite rays.<br />2<br />VERTICAL ANGLES:<br /><ul><li> 1 and 3
  10. 10. 2 and 4</li></ul>1<br />3<br />4<br />LINEAR PAIRS:<br /><ul><li> 1 and 2
  11. 11. C and D</li></ul>D<br />2<br />C<br />1<br />
  12. 12. Corresponding angles<br />Alternate interior angles<br />Alternate exterior angles<br />Vertical angles<br />Linear pair<br />4<br />5<br />9<br />6<br />3<br />2<br />7<br />8<br /> 9 and 3 - Alternate exterior angles<br /> 5 and 7 - Alternate interior angles<br /> 7 and 9 - Vertical angles<br /> 6 and 2 - Alternate interior angles<br /> 4 and 6 - Corresponding angles<br /> 2 and 8 - Corresponding angles<br /> 5 and 4 - Linear Pair<br />

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