<<

Geometry Lesson 1.1.notebook August 21, 2015

Points, Lines, and Planes

In , , , and are considered undefined terms because they are only explained using examples and descriptions.

Undefined Terms

Point ­ a location. It has neither or size. Named using a capitol letter. point A.

Line ­ is made up of points and has no thickness or width. There is exactly one line through any two points. Named by representing two points on the line or a lowercase script letter.

Line m, B

Plane ­ a surface made up of points that extend in all directions. There is exactly one plane through any three points not on the same line. Named with a capitol script letter or by the letters naming three points not on the same line.

Plane K, plane CBD, plane DCB, etc. K

1 Geometry Lesson 1.1.notebook August 21, 2015

Collinear points are points that lie on the same line.

Noncollinear points do not lie on the same line.

Coplanar points lie on the same plane.

Noncoplanar points do not lie in the same plane.

T

V Z n W

X Y

P

r a. Name a line containing point W b. Name a plane containing point X.

What geometric term is modeled by each object? c. Stripe on a sweater d. corner of a box

2 Geometry Lesson 1.1.notebook August 21, 2015

X The intersection of two or more geometric figures is the of points they have in common.

Two lines intersect in a point. Lines can intersect planes and planes can intersect each other.

A l P

m

P is the intersection of line l and m. B Planes A and B intersect in line l. **Better picture at bottom of page 6.

Draw and label a figure for each relationship. a. Lines AB and CD intersect at E for A(­2,4), B(0,­2), b. QR intersects plane T at point S.

C(­3,0), and D(3,3) on a coordinate plane. Point F is

coplanar with these points, but not collinear with AB or CD. c. Ponts J(­4,2), K(3,2), and L are collinear.

3 Geometry Lesson 1.1.notebook August 21, 2015

Definitions or defined terms are explained using undefined terms and/or other defined terms.

Space is defined as a boundless, three­dimensional set of all points. can contain points, lines, and planes. D

K E

J F L

H G

M

a. How many planes appear in this figure? b. Name three points that are collinear

c. Name the intersection of plane HDG with plane X. d. At what point do LM and EF intersect?

4 Geometry Lesson 1.1.notebook August 21, 2015

`

P. 8 13­39, 43­48

5 Geometry Lesson 1.1.notebook August 21, 2015

6