GEOMETRYCHAPTER 1 1-1 Understanding points, lines and planes

Objectives• Students will be able to:• Identify, name, and draw points, lines, segments,

rays,• and planes.• Apply basic facts about points, lines, and planes.

1-1 Understanding lines • The most basic figures in geometry are undefined

terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are the building blocks of geometry.

Collinear Points • Points that lie on the same line are collinear.• Based on the definition. Which points are

collinear? Which are not? K, L, and M are collinear. K, L, and N are noncollinear.

M

K

L

N

Coplanar points • Points that lie on the same plane are coplanar.

Otherwise they are noncoplanar.

• Example of Coplanar

• All the points A, B, C, and D in the plane P are coplanar.

Example 1• Use the following figure to answer the following

questions:• A) Name three collinear pointsAnswer: D,E and F

B) Name Coplanar points Answer: D,E,F and GC)Name a point that is noncollinear and a point that is not coplanar. • Answer: noncollinear is g and noncoplanar is h

Segments and rays

Example 2• Draw a line segment with endpoints a and b

• A B

• Draw ray with endpoint e and pass through d

• D E• Draw line gh • g h

Postulates • A postulate, or axiom, is a statement that is

accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties.

Example 3

Name a line that passes through two pointsAnswer: cd

Name a plane that contains three noncollinear points.

Answer; plane ABC

Intersecting lines • An intersection is the set of all points that two or

more figures have in common. The next two postulates describe intersections involving lines and planes.

Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.

Example 4• Representing Intersections

• A. Sketch two lines intersecting in exactly one point.

B. Sketch a figure that shows a line that lies in a plane.

Homework• Page 9 13-21

Closure • Today we saw about point, lines, lines segments

and rays and how we label them. We also saw collinear and coplanar points. Tomorrow we are going to continue with lesson 1-2.