Download Geo Unit 3

Geometry
Unit 3
Parallel and Perpendicular Lines
Unit III
Unit
3
Angles Formed by Transversal
•
•
•
•
Alternate Interior angles (3 & 6, 4& 5)
Alternate Exterior angles (1 & 8, 2 & 7)
Same-side Interior angles (3 & 5,4 & 6)
Corresponding angles (1 & 5, 3 & 7, 2
& 6, 4 & 8)
1
3
2
4
5
6
7
8
Unit III
Unit
3
Slope
•
y2  y1
m
x2  x1
• Parallel lines have the same slope.
• Perpendicular lines: the product of the two
slopes is -1.
Unit 3III
Unit
Equation of a Line
• Slope intercept form: y = mx + b
• Point-slope form: y2 – y1 = m(x2 – x1)
• Standard form: ax + by = c
Unit III
Unit
3
Intersecting Lines
• Intersecting lines have a point in common.
• Solution is where two equations are equal.
Unit III
Unit
3
Formulas
•
Distance
d
•
x2  x1 2   y2  y1 2
Midpoint
 x1  x2 y1  y2 
,


2 
 2
Unit
Unit3III
Constructing Parallel Lines
• Draw a transversal through one line.
• Use the relationships of angles formed by a
transversal.
• Measure and draw the angle off the transversal
• Draw the parallel line.
Unit III
Unit
3
Proving Lines Parallel
• If two lines are cut by a transversal and a pair of alternate
interior angles is congruent, then the lines are parallel.
• If two lines are cut by a transversal and a pair of alternate
exterior angles is congruent, then the lines are parallel.
• If two lines are cut by a transversal and a pair of same-side
interior angles is supplementary, then the lines are parallel.
• In a plane, two coplanar lines perpendicular to the same line
are parallel.
• Two lines are parallel to a third line are parallel to each other.
Unit III
Unit
3