The document summarizes key concepts about parallel and perpendicular lines including: 1) Parallel lines have the same slope and never intersect, while perpendicular lines have slopes that are negative reciprocals of each other. 2) When lines are cut by a transversal, corresponding angles and alternate exterior angles are congruent for parallel lines, and alternate interior angles are congruent. 3) The slope formula is used to determine if lines are parallel or perpendicular based on their slopes.

1. 3rd Geometry Journal By: IgnacioRodríguez

2. Parallellines/planes and skew lines Parallel lines: two coplanar lines that never intersect. Ex: AB and CD, AC and EG, FH and EG Parallel planes: two planes that never intersect. Ex:[] ABDC and [] EFHG, [] EACG and [] FBDH, [] ABFE and [] CDHG Skew lines: two lines that have no relationship whatsoever. Ex: AC and EF, GH and AE, BD and CG A B E F ([] means plane) C D G H

3. Transversal It is a line that intersects two other lines. EX:

4. AnglesFormed by the Transversal Corresponding: angles that lie in the same side of the transversal. EX: <1and<5, <4and<8, etc. 1 2 Alternate exterior: angles in the 3 4 opposite side of the transversal but in the outside. Ex: <1and<8 and <2and<7 5 6 7 8 Alternate interior: angles in the opposite side of the transversal but in the interior. Ex: <3and<6, <4and <5 Same-side interior: same side of the transversal in the interior. Ex: <3and<5, <4and<6

5. Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Converse: if the pairs of corresponding angles are congruent, then two parallel lines have to be cut by a transversal. Corresponding angles: <1and<5 1 2 <2and<6 3 4 <3and<7 <4and<8 5 6 7 8

6. Alternate Exterior Postulate: If two parallel lines are cut by a transversal, then the pairs of Alternate Exterior angles are congruent. Converse: If the pairs of Alternate Exterior angles are congruent, then two parallel lines were cut by a transversal. Alternate exterior angles: <1and<8 1 2 <2and<7 3 4 5 6 7 8

7. Alternate Interior Postulate: If two parallel lines are cut by a transversal, then the pairs of Alternate Interior angles are congruent. Converse: If the pairs of Alternate Interior angles are congruent, then two parallel lines were cut by a transversal. Alternate exterior angles: <3and<6 1 2 <4and<5 3 4 5 6 7 8

8. Same-Side Interior Postulate: If two parallel lines are cut by a transversal, then the pairs of Same-Side Interior angles are supplementary. Converse: If the pairs of Same-Side Interior angles are Supplementary, then two parallel lines were cut by a transversal. Alternate exterior angles: <3and<5 1 2 <4and<6 3 4 5 6 7 8

9. Perpendicular Transversal Theorem Theorem: If a line is perpendicular to one of the parallel lines, then it must be perpendicular to the other line too. Ex: A _|_ B  A _|_ C I _|_ G  I _|_ Y M _|_ J  M _|_ E A G Y I B I J C E

10. Howdoes the Transative property Apply in Parallel and Perpendicular lines? We know that parallel lines never touch so if line A is parallel to line B and line B is parallal to line C, then line A is parallel to line C. In perpendicular lines this is not possible because if line A is perpendicular to line B and B is perpendicular to line C then line A and line C mudt be parallel. Ex: B B A B C C A C A B C A

11. Slope Slope is the rise of a line over the run of that same line (rise/run) In many equations slope is represented by the lower-case letter m.} Formula: Y¹ –Y² (X,Y) (X,Y) X¹- X² 1 no -1/3 slope 0

12. Slope´srelation With Parallel and Perpendicular lines Parallel: All parallel lines have the same slope as its complementing pair. slopes: line1=1 line1= -1/3 line2=1 line2= -1/3 Perpendicular: All perpendicular lines have the negative reciprocal slope of its complementing pair. slopes: line1= -1/3 line1=1/6 line2= 3/1 line2= -6/1

13. Slope/Intercept Form Formula: Y=mX+b You would use it when the slope and interceps are given. Ex: Y=1X+2 Y=1/2+1 Y=-2/3-2

14. Point/Intercept Form Formula: Y-Y¹= m(X-X¹) You would use it when points are given. Ex: Y-3=1(X+2) Y-0=1/2(X+3) Y+1=(X+0)