Chapter One ReviewFoundations for Geometry

Part 1/4Holt McDougal

©Candace Ho

Understanding Points, Lines, and Planes (Page 6)

1-1

Learning Target 1Identify, name, and draw points, lines, line segments, rays,

and planes, as well as their basic properties.

VocabularyTerm Definition/Name Diagram

Undefined Term Term which cannot be defined by using other figures (eg. Point, line, plane)

No diagram available

Point - Names a location and has no size.

Represented by a dot and capital letter

Line - A straight path that has no thickness and extends forever.

Represented by a lowercase letter or two points on a line

Plane - A flat surface that has no thickness and extends forever

Represented with a script capital letter or three point not on a line

VocabularyTerm Definition/Name Diagram

Collinear (a word to describe) Points that lie on the same line

Coplanar (a word to describe)Points that lie on the same plane

Segment – line segment is part of a line consisting of two points and all points between them

Written with the two endpoints as references

Endpoint – point at one end of a segment or the starting point of a ray

Written with a capital letter

VocabularyTerm Definition/Name Diagram

Ray Written with its endpoint and any other point on the ray

Opposite rays Written with the common endpoint and any other point on each ray

Postulate Statement that is accepted as true without proof

No diagram available

Postulates

Postulate for Points, Line, and Planes

1-1-1 Through any two points there is exactly one line

1-1-2 Through any three noncollinear points there is exactly one plan containing them

1-1-3 If two points lie on a plane, then the line containing those points lies in the plane

Example Diagram

Postulates Continued

Postulate for Intersection of Lines and Planes

1-1-4 If two lines intersect, then they intersect in exactly one point

1-1-5 If two planes intersect, then they intersect in exactly one line

Example Diagram

Basically, all the slides above with the vocabulary and postulates…are very self explanatory. All you have to do, is make sure you KNOW THEM. Because those are the basics and the basics really help you with the further math in this chapter. So take some time to go through the last 5 slides and memorize EVERYTHING.

What you learned so far

So, here in this example, its asking you to name points, lines, and planes. Obviously you know that point is a dot with a capital letter which looks like this

A Line looks like this and in this case you would name the line like b basically represented with a on top of the two points in the line or a lowercase letter

To name a plane, you can name this plane = Plane ABC or with a capital script letter R

Example 1 (page 6)Naming points, lines, and planes

Try Ex. 1 Out!Grab a piece of paper and try these problems out! The answers will b on the last slide of the chapter…so NO CHEATING!Do the problems…then check your answers at the very end of the chapter…HERE WE GO

1. Name 2 points that are on plane S

2. Name the line that passes through Plane T

3. Name Plane S differently

4. Which Plane is point H on?

So, if you look at the vocabulary in this chapter, you will need to know what a segment and a ray looks like and how to draw them.

A segment looks like this and you label segments like this which is basically this on top of the two endpoints of the segments, which in this case is Point A and Point B

Rays look like this and to label it, you

need to identify the endpoint (in example its Point R) and another point on the line. Then put, in this example, RS together and put this on top to label the ray like

Example 2 (page 7)Drawing segments and rays

Opposite rays look like this and you would name it like . First, identify the endpoint (the middle one) which is Point E. Then identify the other two points, one on each ray which is Point F and G . Then put EF and EG underneath the sign.

Example 2 continued

Try Ex. 2 Out!Grab a piece of paper and try these problems out! The answers will b on the last slide of the chapter…so NO CHEATING!Do the problems…then check your answers at the very end of the chapter…HERE WE GODraw the following5. A segment with endpoints F and G6. A ray with endpoint Z that passes through Y

Name the following (e.g. segment or ray/how to name it)7.

8.

S T

So, I think you can do this! Basically you have to name the point and lines in a plane!

In this diagram, the points in the plane would be Point G, H, and F.

The line would be Line n or GH

Example 3 (page 7)Identifying Points and lines in a plane

Try Ex. 3 Out!Grab a piece of paper and try these problems out! The answers will b on the last slide of the chapter…so NO CHEATING!Do the problems…then check your answers at the very end of the chapter…HERE WE GO

Use the figure to name each of the following9. Name a line that contains point B and C10. Name a plane that contains points D, B, and A

So here are two examples of intersection

Example 4 (page 8)Representing Intersection

You can see how the intersection is showed by dotted lines

Try Ex. 4 Out!

11. According to this diagram, plane ________ intersects with plane N.

12. According to this diagram, line m lies on plane_______ but goes straight through plane_________.

Grab a piece of paper and try these problems out! The answers will b on the last slide of the chapter…so NO CHEATING!Do the problems…then check your answers at the very end of the chapter…HERE WE GO

Answers 1. Point H, J, G, and F

works fine (any 2 of those)

2. Line m or HJ or JH 3. Plane HJG or Plane

JGF or Plane GFH… 4. Plane S 5.

6.

7. segment ST 8. Opposite Ray QP and

QR 9. BC or BA 10. Plane DBA or BAC or

CAD or Plane M 11. . According to this

diagram, plane F intersects with plane N.

12. . According to this diagram, line m lies on plane S but goes straight through plane T.

F G

Z Y