1.2 Points, Lines, and Planes

1.2 Points, Lines, and Planes

What is a definition? • Known words used to describe a new word Undefined terms – are terms not formally defined. There are three undefined terms in geometry: 1. Point 2. Line 3. Plane

Point 1. A location in space. 2. Has no dimension (no length, no width, no depth). 3. Usually represented by a dot. 4. Named using one capital letter.

Point For example: ●B

Line • A series of points that extends in opposite directions without end. • One-dimensional (length). • Has an arrowhead on each end representing the fact that it goes on forever. • Always straight. • Named with a lowercase script letter or by 2 points on the line

Line For example: Can be called: Line l Line AB or AB Line BA or BA l A B

Plane • A flat surface that extends forever in two dimensions (length & width). • Contains infinitely many points and lines. • Usually represented by a four-sided figure. • Named with a capital script letter or 3 points on the surface of the plane

Plane For example: Can be named: Plane W Plane ABC, plane BCA, plane CBA, etc. A W C B

More Definitions • Collinear points – points that can lie on the same line.

More Definitions • Noncollinear points – D

More Definitions • Coplanar points – points that can lie on the same plane.

More Definitions • Noncoplanar points – A D

More Definitions • Equidistant – equally distant

More Definitions • Intersect – Two or more figures intersect if they have one or more points in common. • Intersection – All points or sets of points the figures have in common.

When a line and a point intersect, their intersection is a point. l B

When 2 lines intersect, their intersection is a point.

When 2 planes intersect, their intersection is a line.

When a line and plane intersect, their intersection is a point.

Questions???

REMOTE TIME ! Classify each statements as true or false

Question 1 • PF ends at P

Question 2 • Point S is on an infinite number of lines

Question 3 • A plane has no thickness

Question 4 • Collinear points are coplanar

Question 5 • Planes have edges

Question 6 • Two planes intersect in a line segment

Question 7 • Two intersecting lines meet in exactly one point

Question 8 • Points have no size

Question 9 • Line XY can be denoted as XY or YX.

Horizontal Planes – Ceiling and Floor • Horizontal Planes – Two sides horizontal and no sides vertical

Vertical Planes – Walls • Vertical Planes – two sides are vertical

l M O Group Practice Vertical line l intersects a horizontal plane M at point O

Group Practice Horizontal plane Q and vertical plane N intersect

Group Practice Point P is not in Plane N. Three lines through point P intersect N in points A, B, and C.

True or False • All points on a line are coplanar

True or False • A line has one endpoint

True or False • A point is named by a capital letter.

True or False • Two lines intersect in two points.

True or False • The edge of a plane is a line.

1.2 Points, Lines, and Planes