Top Banner
Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts in geometry do not have precise definitions but, we understand their meanings intuitively. We say these concepts are undefined . What are the undefined terms?
15

Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Mar 26, 2015

Download

Documents

Savannah Weeks
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

1

Aim:

Do Now:

1) What is a point?

2) What is a line?

3) What is a plane?

The most fundamental concepts in geometry do not have precise definitions but, we understand their meanings intuitively. We say these concepts are undefined.

What are the undefined terms?

Page 2: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

2

Page 3: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

3

A point indicates a position or location in space.

. P

X

Y

. A(2, 6)

Point:

Points are named using capital letters and/or coordinates.

Page 4: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

4

A line is an infinite set of adjacent points.Line:

Ex: Curved line

Ex: Straight line

Naming a Line:

a) Two points on the line:

b) Single lowercase letter

, , , , ...AB AC BA BC etc�������������������������������������������������������������������������������������������� �������

A B C

m

Page 5: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.
Page 6: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

6

Plane: A plane is a set of points that forms a completely flat surface.

Naming a Plane:

a) Three points on the plane:

b) Single uppercase letter:

A •C•

B •

Plane ABC

R

Plane R

Page 7: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Intersections?

• Lines intersect at a point

• Planes intersect at a line

Page 8: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

8

Def: Collinear Points:A collinear set of points is a set of points all of which lie on the same straight line.

A B C D

E

•Points A, B, C and D are collinear.

•Points A, E and C are not collinear.

Page 9: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

9

Def: Line Segment:

Naming a Line Segment:

Use the names of the endpoints.

A B

“Line segment” AB is part of “Line” AB�������������� �

A line segment is the set of two points on a line called endpoints, and all points on the line between the endpoints.

A B

Page 10: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

10

Measure of Line Segments:

The measure of a line segment is the length of the line segment.

To indicate the “measure” of a line segment, use the name of the line segment without the line above the name.

ABEx: = “measure of line segment”

AB

Ex: The perimeter of ABC is 58 cm.If AB = x - 4, BC = 2x + 8, and CA= x – 2, what is BC? Ans. BC=36 cm

Page 11: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

11

Def: Congruent Line Segments:

Congruent line segments are segments that are equal in measure.

Then AB = CD

E x : I f A B C D , 9 7A B x a n d 4 1 3C D x , w h a t is C D ? A B ?

Ans. CD = 29, AB = 29

Ex: A

C D

B If AB CD

Page 12: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

12

Def: Midpoint The midpoint of a line segment divides the line segment into two congruent segments.

A BM

If M is the midpoint of AB, then: 1)

3)

5)

2)

4)

6)

AM MB AM MB

1

2AM AB

1

2MB AB

2AB AM 2AB MB

Page 13: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

13

Def: Line Bisector The bisector of a line segment is a line that intersects the line segment at its midpoint.

A BM

P

QPMQ�������������� �

is a bisector of AB

If PMQ�������������� � bisects AB at M, then: M is midpoint of AB 1)1)

XM is midpoint of PQ�������������� �? 2)

If PMQ�������������� � intersects AB at its midpoint M, then:

PMQ�������������� �

is a bisector of AB

Page 14: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

14

Addition and Subtraction of Line Segments:

R

P

S

__RS RP

-__RP RS

PS

PS

RS RP PS

RP RS PS

-__PS RS RPPS RS RP

If several line segments belong to the same line, we can write addition and subtraction expressions using the names of these segments.

Page 15: Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.

Geometry Leeson: Undefined Terms, Lines, Line Segments

15

Statement Reason 1) 1) 2) 2) 3) 3)

Simple 2-Column Proof

EPF bisects AB at P

Given

P is the midpt. of AB

Definition of Line Bisector

AP BP Definition of Midpoint

B

Given: EPF bisects AB at P Prove: AP PB

A

FE P