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. • Named using one capital letter. • All geometric figures consist of points • POINTS ARE TO GEOMETRIC FIGURES AS ___________ IS TO HUMANS?

Point For example: ●B What would be a real world example of a point?

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 Real World example?

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. **Planes can be named by more than 3 points, but they must be named in either a clockwise or counter-clockwise manner A W C B Real World example?

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

Vertical Planes – Walls Vertical Planes – two sides are vertical

More Definitions • Collinear points – points that can lie on the same line. **Think of the suffix “CO” as sharing.**

More Definitions • Noncollinear points – D

More Definitions • Coplanar points – What does it mean? points that can lie on the same plane.

More Definitions • If the points do not lie in the same plane they are? • Noncoplanar points – A D

More Definitions • Equidistant – equally distant

Classify each statements as true or false REMOTE TIME !

Question 1 PF ends at P

Question 2 Point S is on an infinite number of lines

Question 3 A plane has no thickness

More Definitions • Intersect – • Two or more figures intersect if they have one or more points in common. • Think “meet” or “Cut” • Intersection – • All points or sets of points the figures have in common. • Depending on what is intersecting, the intersection will be different

When a line and a point intersect, their intersection is a point. l B Like taking a road trip and driving through a certain town or city on the map.

When 2 lines intersect, their intersection is a point. Like the intersection of Foothill and Ramsdale

When 2 planes intersect, their intersection is a line. The planes are cutting through one another

When a line and plane intersect, their intersection is a point. Like sticking a pencil through a piece of paper

Questions???

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.

Partner Share: 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.

1.2 Points, Lines, and Planes