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Aim:. What are the undefined terms ?. Do Now: What is a point? What is a line? 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 . Point:. . A(2, 6). Y. X.

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slide1
Aim:

What are the undefined terms?

  • Do Now:
    • What is a point?
    • What is a line?
    • 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.

Geometry Leeson: Undefined Terms, Lines, Line Segments

point
Point:

. A(2, 6)

Y

X

A point indicates a position or location in space.

. P

Points are named using capital letters and/or coordinates.

Geometry Leeson: Undefined Terms, Lines, Line Segments

slide3
Line:

Ex: Curved line

Ex: Straight line

  • Naming a Line:
    • Two points on the line:
    • Single lowercase letter

A

B

C

m

A line is an infinite set of adjacent points.

Geometry Leeson: Undefined Terms, Lines, Line Segments

plane
Plane:
  • Naming a Plane:
    • Three points on the plane:
    • Single uppercase letter:

B •

C•

Plane ABC

A •

Plane R

R

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

Geometry Leeson: Undefined Terms, Lines, Line Segments

def collinear points
Def: Collinear Points:

E

A

B

C

D

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

  • Points A, B, C and D are collinear.
  • Points A, E and C are notcollinear.

Geometry Leeson: Undefined Terms, Lines, Line Segments

def line segment
Def: Line Segment:

A

B

Naming a Line Segment:

Use the names of the endpoints.

A

B

“Line segment”

is part of “Line”

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

Geometry Leeson: Undefined Terms, Lines, Line Segments

measure of line segments
Measure of Line Segments:

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

Ex:

= “measure of line segment”

Ex: The perimeter of

is 58 cm.

If AB = x - 4, BC = 2x + 8, and CA= x – 2, what is BC?

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

Ans. BC=36 cm

Geometry Leeson: Undefined Terms, Lines, Line Segments

def congruent line segments
Def: Congruent Line Segments:

Ex:

A

B

If

C

D

Congruent line segments are segments that are equal in measure.

Then AB = CD

Ans. CD = 29, AB = 29

Geometry Leeson: Undefined Terms, Lines, Line Segments

def midpoint
Def: Midpoint

M

A

B

1)

3)

5)

2)

4)

6)

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

Geometry Leeson: Undefined Terms, Lines, Line Segments

def line bisector
Def: Line Bisector

Q

A

B

M

P

1)

1)

2)

The bisector of a line segment is a line that intersects the line segment at its midpoint.

X

Geometry Leeson: Undefined Terms, Lines, Line Segments

addition and subtraction of line segments
Addition and Subtraction of Line Segments:

S

P

R

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

Geometry Leeson: Undefined Terms, Lines, Line Segments

simple 2 column proof
Simple 2-Column Proof

B

P

F

E

A

Given

Definition of Line Bisector

Definition of Midpoint

Geometry Leeson: Undefined Terms, Lines, Line Segments