notecards unit 3 parallel and perpendicular lines distance and midpoint equations for lines
TRANSCRIPT
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 //.