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Geometry Journal Chapter 3 By: Alejandro Gonzalez

Geometry Journal Chapter 3 By: Alejandro Gonzalez. Describe parallel lines and parallel planes. Include a discussion of skew lines. Give at least 3 examples. Parallel lines: Lines in the same plane that don't intersect .

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Geometry Journal Chapter 3 By: Alejandro Gonzalez

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  1. Geometry Journal Chapter 3By: Alejandro Gonzalez

  2. Describe parallel lines and parallel planes. Include a discussion of skew lines. Give at least 3 examples. • Parallel lines: Lines in the same plane that don't intersect. • Parallel Planes: Different planes that don't intersect. Planes RSTV and XWZY are parallel Planes RSWX and TVYZ are parallel Planes STXY and WRVZ • Skew lines: Are not coplanar lines that means that lines never intersect and are in different planes.

  3. Describe what a transversal is. Give at least 3 examples. • A transversal is a line that intersects two lines at two different points.

  4. Corresponding, alternate exterior, alternate interior and consecutive interior angles. Give an example of each. • Corresponding: In a transversal, the pair of angles that lay on the same side of the transversal, and on the same side of the other two lines. • Alternate Exterior: In a transversal, the pair of angles that are on the opposite sides of it, and outside the other two lines. • Alternate Interior: In a transversal, the pair of nonadjacent angles that are on the opposite sides of the transversal and between the two other lines. • Consecutive Interior: This are the same as Same side interior angles. There are the angles that are on the same side of the transversal and between the two lines.

  5. Examples: 2 1 Corresponding: <1 and <5 Alternate Exterior: <1 and <8 Alternate Interior: <4 and <5 Consecutive: <3 and <5 4 3 6 5 8 7

  6. Corresponding angle postulate and converse. 2 1 • When two lines are cut by a transversal the corresponding angles are congruent. <1≅<5 <2≅<6 <3≅<7 <4≅<8 4 3 6 5 8 7

  7. Alternate Interior Angles Theorem 2 1 • When the two parallel lines are cut by a transversal the alternate interior angles are congruent. <3≅<6 <4≅<5 4 3 6 5 8 7

  8. Same Side interior angle theorem 2 1 • When the two parallel lines are cut by a transversal the same side interior angles are congruent. <3≅<5 <4≅<6 4 3 6 5 8 7

  9. Alternate Exterior Angles Theorem 2 1 • When two parallel lines are cut by the transversal the alternate exterior angles are congruent <1≅<8 <2≅<7 4 3 6 5 8 7

  10. Perpendicular Transversal Theorem • In a plane, If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line also.

  11. The Transitive Property in parallel and perpendicular lines • Parallel: If two lines are parallel to a third line then the two lines are parallel to each other. • Perpendicular: If two lines are perpendicular to a third line then they are parallel to each other.

  12. Slope • To find the slope of a line you need to use the formula EX 1: (2 , 1) , (4 , 5) m= ( 5 - 1 ) / (4 - 2) = 4 / 2 = 2 EX 2: (-1 , 0) , (3 , -5) m= ( -5 - 0 ) / ( 3 - (-1) ) = -5 / 4 EX 3: (2 , 1) , (-3 , 1) m = ( 1 - 1 ) / ( -3 - 2 ) = 0 EX 4: (-1 , 2) , (-1 ,- 5) m = ( -5 - 2 ) / ( -1 - (-1)

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