Chapter 3.1 Notes

Parallel Lines – 2 lines that do not intersect and are coplanar Parallel Planes – 2 planes that do not intersect Skew Lines – 2 lines that do not intersect and are not coplanar

Parallel Postulate – If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

If then Perpendicular Postulate – If there is a line and a point not on the line then there is exactly one line through the point and perpendicular to the given line If then

Identifying Angles Formed by Transversals Transversal – is a line that intersects 2 or more coplanar lines at different points.

Transversal

Corresponding Angles 1 2 3 4 Alternate Interior Angles 5 6 7 8 Alternate Exterior Angles Consecutive Interior Angles (Same-Side Int. Angles)

Chapter 3.2 Notes

Flow Proof – uses arrows to show the flow of the logical argument.

Thm – if 2 lines intersect to form a linear pair of congruent angles, then they are perpendicular.

If then Thm – if 2 sides of 2 adjacent acute angles are perpendicular, then the angles are complementary.

If then 1 2 m ∠ 1 + m ∠ 2 = 90°

Thm – If 2 lines are perpendicular, then they intersect to form four right angles If then

Chapter 3.3 Notes

Corresponding ∠ Post.

Alt. Int. ∠ Thm Alt. Ext. ∠ Thm Cons. Int. ∠ Thm

Perpendicular Thrasversal Thm – If a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other.

If then

Chapter 3.4 Notes

Four ways to prove two lines are parallel.

1) Show Corr. ∠’s are ≌ 2) Show Alt. Int. ∠’s are ≌ 3) Show Alt. Ext. ∠’s are ≌ 4) Show Same Side are Supp.

(Cons. Int. ∠’s are supp.)

Chapter 3.5 Notes

Thm – Is 2 lines are parallel to the same line then they are parallel to each other.

* If p II q and q II r, then p II r. p q r Thm – In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.

* If m ⊥ p and n ⊥ p, then m II n.

Slope = Rise Run

Chapter 3.6 Notes

m = y – y 1 x – x 1 y = mx + b Two lines are parallel if they have the same slope.

Chapter 3.7 Notes

2 Lines are Perpendicular to each other if their slopes are negative reciprocals of each other.

Ex. m = 2/3 and m 1 perpendicular lines = -3/2 then they would be