Successfully reported this slideshow.
Upcoming SlideShare
×

Geo journal 3

452 views

Published on

M2 3rd Geometry Journal!

Published in: Education
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Geo journal 3

1. 1. 3rd Geometry<br />Journal <br />By: IgnacioRodríguez<br />
2. 2. Parallellines/planes<br /> and skew lines<br />Parallel lines: two coplanar lines that never intersect.<br />Ex: AB and CD, AC and EG, FH and EG<br />Parallel planes: two planes that never intersect.<br />Ex:[] ABDC and [] EFHG, [] EACG and [] FBDH, [] ABFE and [] CDHG<br />Skew lines: two lines that have no relationship whatsoever.<br />Ex: AC and EF, GH and AE, BD and CG<br /> A B<br /> E F<br />([] means plane)<br /> C D<br /> G H<br />
3. 3. Transversal<br />It is a line that intersects two other lines.<br />EX:<br />
4. 4. AnglesFormed<br />by the Transversal<br />Corresponding: angles that lie in <br />the same side of the transversal.<br />EX: <1and<5, <4and<8, etc. <br /> 1 2<br />Alternate exterior: angles in the 3 4<br />opposite side of the transversal <br />but in the outside. <br />Ex: <1and<8 and <2and<7 5 6 <br /> 7 8<br />Alternate interior: angles in the opposite<br />side of the transversal but in the interior.<br />Ex: <3and<6, <4and <5<br />Same-side interior: same side of the transversal in the interior.<br />Ex: <3and<5, <4and<6<br />
5. 5. Corresponding Angles<br />Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.<br />Converse: if the pairs of corresponding angles are congruent, then two parallel lines have to be cut by a transversal.<br />Corresponding angles: <br /><1and<5 1 2<br /> <2and<6 3 4<br /><3and<7<br /><4and<8<br /> 5 6<br /> 7 8<br />
6. 6. Alternate Exterior<br />Postulate: If two parallel lines are cut by a transversal, then the pairs of Alternate Exterior angles are congruent.<br />Converse: If the pairs of Alternate Exterior angles are congruent, then two parallel lines were cut by a transversal.<br />Alternate exterior angles: <br /><1and<8 1 2<br /> <2and<7 3 4<br /> 5 6<br /> 7 8<br />
7. 7. Alternate Interior<br />Postulate: If two parallel lines are cut by a transversal, then the pairs of Alternate Interior angles are congruent.<br />Converse: If the pairs of Alternate Interior angles are congruent, then two parallel lines were cut by a transversal.<br />Alternate exterior angles: <br /><3and<6 1 2<br /> <4and<5 3 4<br /> 5 6<br /> 7 8<br />
8. 8. Same-Side Interior<br />Postulate: If two parallel lines are cut by a transversal, then the pairs of Same-Side Interior angles are supplementary.<br />Converse: If the pairs of Same-Side Interior angles are Supplementary, then two parallel lines were cut by a transversal.<br />Alternate exterior angles: <br /><3and<5 1 2<br /> <4and<6 3 4<br /> 5 6<br /> 7 8<br />
9. 9. Perpendicular<br />Transversal Theorem<br />Theorem: If a line is perpendicular to one of the parallel lines, then it must be perpendicular to the other line too.<br />Ex:<br /> A _|_ B  A _|_ C I _|_ G  I _|_ Y M _|_ J  M _|_ E <br /> A G Y I<br />B<br /> I J<br />C<br /> E<br />
10. 10. Howdoes the<br />Transative property<br />Apply in Parallel and<br />Perpendicular lines?<br />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.<br />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.<br />Ex: B B A B C<br />C<br /> A C A<br />B<br /> C A <br />
11. 11. Slope<br />Slope is the rise of a line over the run of that same line (rise/run)<br />In many equations slope is represented by the lower-case letter m.}<br />Formula: Y¹ –Y² (X,Y) (X,Y)<br /> X¹- X²<br /> 1 no -1/3 <br /> slope 0<br />
12. 12. Slope´srelation<br />With Parallel and <br />Perpendicular lines<br />Parallel: All parallel lines have the <br />same slope as its complementing pair.<br /> slopes: line1=1 line1= -1/3<br /> line2=1 line2= -1/3<br />Perpendicular: All perpendicular lines <br />have the negative reciprocal slope of its<br />complementing pair.<br /> slopes: line1= -1/3 line1=1/6 <br /> line2= 3/1 line2= -6/1 <br />
13. 13. Slope/Intercept<br />Form<br />Formula: Y=mX+b<br />You would use it when the slope and interceps are given.<br />Ex:<br /> Y=1X+2 Y=1/2+1 Y=-2/3-2<br />
14. 14. Point/Intercept<br />Form<br />Formula: Y-Y¹= m(X-X¹)<br />You would use it when points are given.<br />Ex:<br />Y-3=1(X+2) Y-0=1/2(X+3) Y+1=(X+0)<br />