Notecards Unit 3

Parallel and Perpendicular Lines

Distance and MidpointEquations for Lines

Notecard 49

Definition of Parallel Lines (//)

Two lines that lie in the same plane that never intersect are called parallel.Lines m & n are parallel

Notecard 50

Definition of Skew Lines

Two lines are skew if they do not intersect and do not lie in the same plane. Lines m & k are skew

Notecard 51

Definition of Parallel PlanesTwo planes that do not intersect.

Planes T & U are parallel

Notecard 52

• Definition of Perpendicular LinesPerpendicular lines are lines that intersect to form a right angle.Line CD and Line DE are perpendicular

Notecard 53

• Definition of Perpendicular Planes

Planes that intersect to form a right angle.Planes ABC and ABG are perpendicular.

Notecard 54

Parallel PostulateIf 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. There is exactly one line through P parallel to line m.

Notecard 55

Perpendicular PostulateIf there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. There is exactly one line through P perpendicularto line m.

Notecard 56

• Transitive Property of Parallel Lines

If two lines are // to the same line, then they are // to each other.

Notecard 57

Slope – the change in y divided by the change in x

Formula: Slope = y2 – y1

x2 – x1

Notecard 58

Postulate – Slope of Parallel LinesIn a coordinate plane, two non-vertical lines are // if and only if they have the same slope. Any two vertical lines are parallel.

Notecard 59

Postulate – Slope of Perpendicular LinesIn a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is -1. (They are negative reciprocals.)Horizontal lines are perpendicular to vertical lines.

Notecard 60

Definition of Midpoint & FormulaThe point that divides a segment into two congruent segments.

Midpoint = 1 2 1 2,2 2

x x y y

Notecard 61

Distance Formula: the ditance between two points (x1, y1) and (x2, y2)

d = 2 2

2 1 2 1( ) ( )x x y y

Notecard 62

Definition – Distance from a point to a LineThe distance between a point and a line must be measured with a segment from the point to the line.

Notecard 63

Definition – Distance between 2 Parallel LinesThe distance between 2 // lines must be measured with a segment to both lines.

Notecard 64

TheoremIf 2 lines intersect to form a linear pair of congruent angles, then the lines are . Lines g & h are

Notecard 65

TheoremIf two lines are , then they intersect to form 4 right angles. Angles 1, 2, 3, & 4 are all right angles.

Notecard 66

TheoremIf two sides of two adjacent acute angles are , then the angles are complementary. Angles 1 & 2 are complementary

Notecard 67

Perpendicular Transversal TheoremIf a transversal is to one of two // lines, then it is perpendicular to the other.

If line j line h and line h and line k are //, then line j line k

Notecard 68

Lines Perpendicular to a Transversal TheoremIn a plane, if 2 lines are to the same line, then they are // to each other.

If lines m & n are both to line p, then lines m & n are //.