M2 3rd Geometry Journal!

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)