Lesson1-2notetakingguide

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GeomPHM5e_DNG_002-024

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1:54 PM

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Name_____________________________________ Class____________________________ Date________________

Lesson 1-2 (pp. 10–16)

Points, Lines, and Planes

Lesson Objectives 1 Understand basic terms of geometry 2 Understand basic postulates of geometry

NAEP 2005 Strand: Geometry Topic: Dimension and Shape Local Standards: ____________________________________

Vocabulary and Key Concepts. Postulate 1-1 Through any two points there is All rights reserved.

t B

Line t is the only line that passes through points A and

.

A Postulate 1-2 If two lines intersect, then they intersect in A D

B

C

E

*AE )

*

)

and BD intersect at

.

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

Postulate 1-3 If two planes intersect, then they intersect in

S

R T W

Plane RST and plane STW intersect in

*ST)

.

Postulate 1-4 Through any three noncollinear points there is A point is Space is A line is A

B

t

Collinear points are

Geometry Daily Notetaking Guide

Lesson 1-2

5

GeomPHM5e_DNG_002-024

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Name_____________________________________ Class____________________________ Date ________________

A plane is

B C A Plane ABC

Two points or lines are coplanar if A postulate or axiom is

Examples. X

1 Identifying Collinear Points In the figure at right, name three points that are collinear and three points that are not collinear. ,

, and

lie on a line, so they are

collinear.

m

Z

Y

All rights reserved.

Points

W

Any other set of three points in the figure do not lie on a line, so no other set of three points is collinear. For example, X, Y, and Z form a

and are not collinear. U

R

2 Naming a Plane Name the plane shown in two different ways.

Some possible names for the plane shown are the following: plane

, plane

plane

, and plane

, plane

T

S

,

. H

3 Finding the Intersection of Two Planes Use the diagram at right. What is the intersection of plane HGC and plane AED?

E

G F

As you look at the cube, the front face is on plane AEFB, the back face is on plane HGC, and the left face is on plane AED. The back and left faces of the cube intersect at vertically at

6

Lesson 1-2

. Planes HGC and AED intersect

C

D A

B

.

Geometry Daily Notetaking Guide

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

You can name a plane using

GeomPHM5e_DNG_002-024

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Name_____________________________________ Class____________________________ Date ________________

4 Using Postulate 1-4 Shade the plane that contains X, Y, and Z.

Z

Points X, Y, and Z are the vertices of one of the four triangular faces of the pyramid. To shade the plane, shade the interior of the triangle formed by , , and .

Y

X

V

W

Check Understanding.

All rights reserved.

1. Use the figure in Example 1. a. Are points W, Y, and X collinear?

b. Name line m in three different ways.

c. Critical Thinking Why do you think * ) arrowheads are used when drawing a line or naming a line such as ZW ?

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

2. List three different names for plane Z.

H

G

Z E

* )

3. Name two planes that intersect in BF .

F H

E

G F C

D A 4. a. Shade plane VWX. Z

Y V

B

b. Name a point that is coplanar with points V, W, and X.

X W

Geometry Daily Notetaking Guide

Lesson 1-2

7