lesson 1.3 undefined terms and definitions pp. 9-13 lesson 1.3 undefined terms and definitions pp....

Lesson 1.3Undefined Terms and

Definitionspp. 9-13

Lesson 1.3Undefined Terms and

Definitionspp. 9-13

Objectives:1. To identify characteristics of a

good definition.2. To recognize and visualize the

undefined terms of geometry.

Objectives:1. To identify characteristics of a

good definition.2. To recognize and visualize the

undefined terms of geometry.

1.1. Clear -Clear - The definition must The definition must communicate the point and communicate the point and state the term beingstate the term beingdefined, avoiding vague or defined, avoiding vague or ambiguous language.ambiguous language.

1.1. Clear -Clear - The definition must The definition must communicate the point and communicate the point and state the term beingstate the term beingdefined, avoiding vague or defined, avoiding vague or ambiguous language.ambiguous language.

Characteristics of Good Definitions




2.2. Useful -Useful - The definition The definition must use only words that must use only words that have been previously have been previously defined or are commonly defined or are commonly accepted as undefined.accepted as undefined.

2.2. Useful -Useful - The definition The definition must use only words that must use only words that have been previously have been previously defined or are commonly defined or are commonly accepted as undefined.accepted as undefined.



3.3. Precise -Precise - The definition The definitionmust be accurate andmust be accurate andreversible, identify thereversible, identify theclass to which class to which the object the object belongs, and its belongs, and its distinguishing traits.distinguishing traits.

3.3. Precise -Precise - The definition The definitionmust be accurate andmust be accurate andreversible, identify thereversible, identify theclass to which class to which the object the object belongs, and its belongs, and its distinguishing traits.distinguishing traits.

4.4. Concise -Concise - The definition The definitionmust be a good sentencemust be a good sentenceand use good grammar. and use good grammar. It should stick to the pointIt should stick to the pointand avoid unnecessaryand avoid unnecessarywords.words.

4.4. Concise -Concise - The definition The definitionmust be a good sentencemust be a good sentenceand use good grammar. and use good grammar. It should stick to the pointIt should stick to the pointand avoid unnecessaryand avoid unnecessarywords.words.





5.5. Objective -Objective - The definition The definitionmust be neutral. Avoidmust be neutral. Avoidemotional words, figures ofemotional words, figures ofspeech, and limitations ofspeech, and limitations oftime or place.time or place.

5.5. Objective -Objective - The definition The definitionmust be neutral. Avoidmust be neutral. Avoidemotional words, figures ofemotional words, figures ofspeech, and limitations ofspeech, and limitations oftime or place.time or place.

Example 1 Evaluate this definition. Space is the set of all points.

Example 1 Evaluate this definition. Space is the set of all points.

To determine if this is a good To determine if this is a good definition of space, we need to definition of space, we need to analyze each of the five analyze each of the five characteristics. characteristics.

To determine if this is a good To determine if this is a good definition of space, we need to definition of space, we need to analyze each of the five analyze each of the five characteristics. characteristics.

1. Clear. The object being defined is named in the definition. It is not ambiguous.

1. Clear. The object being defined is named in the definition. It is not ambiguous.

Example 1Example 1

2. Useful. Look at all the words in the definition. Have they all been defined? At this point in our study, we must say no. The word set was discussed in the first two sections of the chapter, but has the word point been defined?

2. Useful. Look at all the words in the definition. Have they all been defined? At this point in our study, we must say no. The word set was discussed in the first two sections of the chapter, but has the word point been defined?

Example 1Example 1

3. Precise. The definition describes space accurately. Space is classified as a set and is described as the particular set containing all points. The definition is also reversible. We could say, “The set of all points is space.”

3. Precise. The definition describes space accurately. Space is classified as a set and is described as the particular set containing all points. The definition is also reversible. We could say, “The set of all points is space.”

Example 1Example 1

4. Concise. This definition contains only necessary words and uses proper grammar.

4. Concise. This definition contains only necessary words and uses proper grammar.

Example 1Example 1

5. Objective. This definition uses appropriate objective language.

5. Objective. This definition uses appropriate objective language.

In geometry there are three In geometry there are three undefined terms that can be undefined terms that can be described but not defined:described but not defined:

1.1. PointPoint2.2. LineLine3.3. PlanePlane

In geometry there are three In geometry there are three undefined terms that can be undefined terms that can be described but not defined:described but not defined:

1.1. PointPoint2.2. LineLine3.3. PlanePlane

PointPointDescription: Description: Spot; an object with no Spot; an object with no dimensions, length, width, or dimensions, length, width, or thickness; a location in space. thickness; a location in space.

Notation:Notation: denoted by a capital letter, denoted by a capital letter, location marked by a dot location marked by a dot ••PP

PointPointDescription: Description: Spot; an object with no Spot; an object with no dimensions, length, width, or dimensions, length, width, or thickness; a location in space. thickness; a location in space.

Notation:Notation: denoted by a capital letter, denoted by a capital letter, location marked by a dot location marked by a dot ••PP

LineLineDescription: Description: Straight; an object that Straight; an object that extends infinitely in one dimension; extends infinitely in one dimension; has length but no width or thickness. has length but no width or thickness.

Notation:Notation: CDCD; or a lowercase script ; or a lowercase script letter letter mm

LineLineDescription: Description: Straight; an object that Straight; an object that extends infinitely in one dimension; extends infinitely in one dimension; has length but no width or thickness. has length but no width or thickness.

Notation:Notation: CDCD; or a lowercase script ; or a lowercase script letter letter mm

CC DDmm

kk

PlanePlaneDescription: Description: Flat; an object that Flat; an object that extends infinitely in two dimensions; extends infinitely in two dimensions; has length and width but no has length and width but no thickness. thickness.

Notation:Notation: plane plane kk; denoted by a lower ; denoted by a lower case lettercase letter

PlanePlaneDescription: Description: Flat; an object that Flat; an object that extends infinitely in two dimensions; extends infinitely in two dimensions; has length and width but no has length and width but no thickness. thickness.

Notation:Notation: plane plane kk; denoted by a lower ; denoted by a lower case lettercase letter

HomeworkHomeworkpp. 11-13pp. 11-13

HomeworkHomeworkpp. 11-13pp. 11-13

►►A. ExercisesA. Exercises1.1. A frog is an amphibian.A frog is an amphibian.

►►A. ExercisesA. Exercises1.1. A frog is an amphibian.A frog is an amphibian.

1.1. Not clearNot clear2.2. Not useful Not useful 3.3. Not objectiveNot objective4.4. Not preciseNot precise5.5. Good definitionGood definition

(not reversible)(not reversible)

►►A. ExercisesA. Exercises2.2. A noun is a word used to name a A noun is a word used to name a

person, place, thing, quality, or person, place, thing, quality, or action.action.

►►A. ExercisesA. Exercises2.2. A noun is a word used to name a A noun is a word used to name a

person, place, thing, quality, or person, place, thing, quality, or action.action.


►►A. ExercisesA. Exercises3.3. A glove is a covering for the A glove is a covering for the

hand.hand.

►►A. ExercisesA. Exercises3.3. A glove is a covering for the A glove is a covering for the

hand.hand.


(not reversible)(not reversible)

►►A. ExercisesA. Exercises4.4. Plasma is the clear, yellowish Plasma is the clear, yellowish

liquid part of the blood.liquid part of the blood.

►►A. ExercisesA. Exercises4.4. Plasma is the clear, yellowish Plasma is the clear, yellowish

liquid part of the blood.liquid part of the blood.


►►A. ExercisesA. Exercises5.5. Nine is the sum of six and three.Nine is the sum of six and three.

►►A. ExercisesA. Exercises5.5. Nine is the sum of six and three.Nine is the sum of six and three.


(words not defined)(words not defined)

►►A. ExercisesA. Exercises6.6. An empty set is any set.An empty set is any set.

►►A. ExercisesA. Exercises6.6. An empty set is any set.An empty set is any set.

1.1. Not clearNot clear2.2. Not useful Not useful 3.3. Not objectiveNot objective4.4. Not conciseNot concise5.5. Good definitionGood definition

(doesn’t comm. pt.)(doesn’t comm. pt.)

►►A. ExercisesA. Exercises7.7. An atheist is like when some An atheist is like when some

crazy nut denies that God exists.crazy nut denies that God exists.

►►A. ExercisesA. Exercises7.7. An atheist is like when some An atheist is like when some

crazy nut denies that God exists.crazy nut denies that God exists.


(bad grammar)(bad grammar)(crazy nut)(crazy nut)

►►A. ExercisesA. Exercises8.8. Love is unselfish concern for the Love is unselfish concern for the

best interests of another.best interests of another.

►►A. ExercisesA. Exercises8.8. Love is unselfish concern for the Love is unselfish concern for the

best interests of another.best interests of another.


►►A. ExercisesA. Exercises9.9. A retable is a reredos. A retable is a reredos.

►►A. ExercisesA. Exercises9.9. A retable is a reredos. A retable is a reredos.


(reredos undefined)(reredos undefined)

►►A. ExercisesA. Exercises10.10. Braille is a system of writing and printing Braille is a system of writing and printing

for blind people that consists of different for blind people that consists of different patterns of raised dots that represent patterns of raised dots that represent letters, words, numbers, and punctuation. letters, words, numbers, and punctuation.

►►A. ExercisesA. Exercises10.10. Braille is a system of writing and printing Braille is a system of writing and printing

for blind people that consists of different for blind people that consists of different patterns of raised dots that represent patterns of raised dots that represent letters, words, numbers, and punctuation. letters, words, numbers, and punctuation.


(wordy)(wordy)

►A. ExercisesIllustrate each idea.11. point K

►A. ExercisesIllustrate each idea.11. point K

►A. ExercisesIllustrate each idea.13. line l

►A. ExercisesIllustrate each idea.13. line l

►A. ExercisesWrite a sentence describing each illustration.15.


nn FF



ll

QQ

State in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.34. A = {1, 3, 5}

B = {x|x is an odd integer}

State in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.34. A = {1, 3, 5}

B = {x|x is an odd integer}

■ Cumulative Review■ Cumulative Review

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.35. A = {x|x is a prime number greater

than 2}B = {x|x is an even integer}

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.35. A = {x|x is a prime number greater

than 2}B = {x|x is an even integer}

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.36. A = {x|x is the square of an

integer}B = {0, 1, 4, 9, 16, 25, . . .}

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.36. A = {x|x is the square of an

integer}B = {0, 1, 4, 9, 16, 25, . . .}

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.37. A = {1, 11, 21, 31}

B = {-11, 1, 11, 121, 1331}

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.37. A = {1, 11, 21, 31}

B = {-11, 1, 11, 121, 1331}

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.38. A = {x|x > 2}

B = {x|x ≤ 2}

■ Cumulative ReviewState in words the most specific relationship that you can between each pair of sets. Express as many of the relations in symbols as you can. Consider the integers as the universal set.38. A = {x|x > 2}

B = {x|x ≤ 2}

Analytic GeometryAnalytic Geometry

Graphing PointsGraphing Points

Analytic GeometryAnalytic Geometry makes a makes a connection between the connection between the figures that you see in figures that you see in geometry and the equations geometry and the equations that you saw in algebra.that you saw in algebra.

Cartesian planeCartesian plane

originoriginxx

yy

IIIIII

IIIIII IVIV

Plot the point (3, -2)Plot the point (3, -2)

xx

yy

(3, -2)(3, -2)

Give the coordinate of each point.Give the coordinate of each point.

xx

yy

BBAA

CC

(5, 2)(5, 2)(-3, 3)(-3, 3)

(0, -2)(0, -2)

Plot the following points.Plot the following points.

xx

yy

1.1. (-1,4) (-1,4) 2.2. (2,2)(2,2)3.3. (0,-2)(0,-2)4.4. (3,-2)(3,-2)5.5. ((33//22,1) ,1)

1.1. (-1,4) (-1,4) 2.2. (2,2)(2,2)3.3. (0,-2)(0,-2)4.4. (3,-2)(3,-2)5.5. ((33//22,1) ,1)

11

22

33 44

55

lesson 1.3 undefined terms and definitions pp. 9-13 lesson 1.3 undefined terms and definitions pp....

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