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Geometry Journal

Geometry Journal. Sebastian Busto 9-3. Parallel lines and planes; skew segments. Two parallel lines are two lines on the same plane that don’t intersect Two parallel planes are 2 planes that don’t intersect. Parallel lines: EB || AC EF || GH BD|| FH. Parallel Planes: A BF || CDH

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Geometry Journal

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  1. Geometry Journal Sebastian Busto 9-3

  2. Parallel lines and planes; skew segments Two parallel lines are two lines on the same plane that don’t intersect Two parallel planes are 2 planes that don’t intersect Parallel lines: EB || AC EF || GH BD|| FH Parallel Planes: ABF || CDH EFG || ACD EAC || FBD F H E G Skew segments: EA|| FH BA|| HD BD|| AE D B A C

  3. Parallel and Perpendicular Postulate Parallel Postulate : There is one and only one line through C and it is parallel to AB Example: Given A line AB and a point C not on the line. Perpendicular Postulate : There is one and only one line through C and it is perpendicular to AB

  4. Transversal A transversal is a line that crosses two or more line in different points.

  5. Corresponding, alternate exterior, alternate interior and consecutive interior angles Corresponding: are in the same position like A and E A B C D E F GH Alternate exterior: exterior sides opposite positions like G and B Alternate exterior: interior side opposite positions like E and D Consecutive interior: Same side of the transversal like C and E

  6. Corresponding angle theorem When two parallel lines are cut by a transversal the corresponding angles are congruent. 12 34 56 7 8

  7. Alternate interior theorem When two parallel lines are cut by a transversal the alternate interior angles are congruent. 12 34 56 7 8

  8. Consecutive interior theorem When two parallel lines are cut by a transversal the consecutive interior angles are congruent. 12 34 56 7 8

  9. Alternate exterior theorem When two parallel lines are cut by a transversal the alternate exterior angles are congruent. 12 34 56 7 8

  10. Perpendicular Transversal Theorem If a transversal is perpendicular to one line then it is perpendicular to any parallel to that line. A B Interior: C=F , D =E Exterior: A=H , D=G Consect: C=E , D=F C D E F GH

  11. Transitive Property 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 Slope: of a line using formula 1) (1, -4) + (-4, 2) = 2) (2, -3) + (-3, 3) = 3) (1, -4) + (-4, 2) =

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