1. Geometry Journal 3 Michelle Habie

2. Parallel Lines & Planes *Skew Lines:
Parallel Lines: are coplanar and do not intersect, always keeping the same distance from each other. Parallel Planes: two planes that do not intersect. Skew Lines: Lines that do not intersect and are not coplanar and will never touch each other. Examples:
Side-walk for a handicap
Mirror:

3. Transversal:
Line that intersects two parallel lines at two different points. The transversal “t” and other two lines “r” and “s” forming special pairs of angles such as: corresponding, alternate exterior & interior and same side interior. (eight angles.) t s 1 2 3 4 r 5 6 7 8

4. Angles:
Corresponding: Lie on the same side of the transversal. One inside and one outside the parallel lines. Alternate Exterior: Lie on opposite sides of the transversal outside the paralleles. Alternate Interior: Not adjacent angles that lie on the opposite sides of the transversal inside the parallel lines. Same-side Interior: Are the angle pair that are on the inside of the two parallel lines forming a pair of supplementary angles.
Alternate Exterior:
Alternate Interior:
Corresponding:
Same- Side Interior:

5. Corresponding Angles Postulate & converse:
If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel. Examples:
1 & 5
2 & 6
3 & 7
4 & 8 1 2 3 4 5 6 8
Trains Transversal via 7

6. Alternate Interior Angles Theorem & converse:
If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel. Examples:
Electric stairs in mall 
Parking Lot

7. Same- Side Interior Angles Theorem & Converse:
If two coplanar lines are cut by a transversal so that a pair of same- side interior angles are supplementary, then the two lines are parallel. Examples:
Boxing Ring:
Neighbors

8. Alternate Exterior Angles Theorem & Converse:
If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel. Examples:
Airport:
Supermarket halls (baskets):

9. Perpendicular Transversal Theorems:
In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other parallel line. Examples:
If p is perpendicular to s and q is perpendicular to s then p and q are parallel.
If room a has lines m and n perpendicular to l then, o and q are also perpendicular to l. a b d l q
If a is perpendicular to c and b is perpendicular to c then a is perpendicular to c. a b c c a s t m n o p q r

10. Transitive Property:
Parallel Lines: If one line is parallel to the second one and that second one is parallel to a third one then, the three lines are parallel to each other. Perpendicular Lines: If p is perpendicular to q and r is perpendicular to q also, then p and r must be parallel. Perpendicular Lines Theorem: If two intersecting lines form a linear pair of congruent angles then the lines must be perpendicular. Examples:
If line l is parallel to line m and line m is parallel to line n then, l and n are also parallel. m l n a
If a is perpendicular to c and a is parallel to b then b is perpendicular to c. b

11. Slope of a Line:
How to find the slope of a line? You need to have atleast 2 points or a graph of a line to be able to find the vertical change over the horizontal change.(rise/run) Formula: m=y2-y1/ x2- x1 Parallel Lines: Two parallel lines must have same slope. Perpendicular Lines: Have opposites and reciprocal slopes.

12. examples perpendicular:
M=y2-y1/x2-x1 = (3)- (-1) / (-1)- (1)= 4/2= -2 Y-y1= m (x-x1) Y-(-1)=-2 (x-1) y+1= -2x+2 Y=-2x+1 4x+2y=6 2y= 4x+6 Y=-2x+3 M=-2 Y-y1=m (x-x1) Y-(-1)=-2 (x-2) Y+1=-2x+4
Y-5= -2/5x=6/5
Y=-2/5x=6/5+5
Y=-2/5x+31/5

13. Examples of Parallel:
(6,-1) mll=1/2 Y-y1=m (x-x1) Y-(-1)=1/2 (x-6) Y+1=1/2 x-3 Y+1-1=1/2 x Y=1/2x-4 M=y2-y1/ x2-x1= (-1)-3/ 2-(-2)= -1-3/2+2 =-4/4 =-1
Y=(-5)= -4/3 (x-2)
Y+5= -4/3x+ 8/3
3y+15 = -4x+8
4x+3y=-7

14. Equations:
Slope Intercept Form: To write an equation in this form you must know the slope and atleast one point in order to find the y- intercept. Formula: y=mx+b Point Slope Form: It is used to write an equation when knowing the slope and a point that crosses the line. Formula: (y-y1) =m (x-x1) When to use each form: Slope Intercept Form: is useful when you need to graph the line. Point Slope Form: is useful when ever you have to write an equation. Real Life Situations are: Business Sells, construction Growth of Population

15. Examples:
Slope- Intercep Form:

16. Point- Slope Form: