Lesson 1 3 Undefined Terms and Definitions pp

Lesson 1. 3 Undefined Terms and Definitions pp. 9 -13

Objectives: 1. To identify characteristics of a good definition. 2. To recognize and visualize the undefined terms of geometry.

Characteristics of Good Definitions 1. Clear - The definition must communicate the point and state the term being defined, avoiding vague or ambiguous language.

Characteristics of Good Definitions 2. Useful - The definition must use only words that have been previously defined or are commonly accepted as undefined.

Characteristics of Good Definitions 3. Precise - The definition must be accurate and reversible, identify the class to which the object belongs, and its distinguishing traits.

Characteristics of Good Definitions 4. Concise - The definition must be a good sentence and use good grammar. It should stick to the point and avoid unnecessary words.

Characteristics of Good Definitions 5. Objective - The definition must be neutral. Avoid emotional words, figures of speech, and limitations of time or place.

Example 1 Evaluate this definition. Space is the set of all points. To determine if this is a good definition of space, we need to analyze each of the five characteristics.

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

Example 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?

Example 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. ”

Example 1 4. Concise. This definition contains only necessary words and uses proper grammar. 5. Objective. This definition uses appropriate objective language.

In geometry there are three undefined terms that can be described but not defined: 1. Point 2. Line 3. Plane

Point Description: Spot; an object with no dimensions, length, width, or thickness; a location in space. Notation: denoted by a capital letter, location marked by a dot • P

Line Description: Straight; an object that extends infinitely in one dimension; has length but no width or thickness. Notation: CD; or a lowercase m script letter m C D

Plane Description: Flat; an object that extends infinitely in two dimensions; has length and width but no thickness. Notation: plane k; denoted by a lower case letter k

Homework pp. 11 -13

►A. Exercises 1. A frog is an amphibian. 1. Not clear 2. Not useful 3. Not objective 4. Not precise (not reversible) 5. Good definition

►A. Exercises 2. A noun is a word used to name a person, place, thing, quality, or 1. Not clear action. 2. Not useful 3. Not objective 4. Not precise 5. Good definition

►A. Exercises 3. A glove is a covering for the hand. 1. Not clear 2. Not useful 3. Not objective 4. Not precise (not reversible) 5. Good definition

►A. Exercises 4. Plasma is the clear, yellowish liquid part of the blood. 1. Not clear 2. Not useful 3. Not objective 4. Not precise 5. Good definition

►A. Exercises 5. Nine is the sum of six and three. 1. Not clear 2. Not useful (words not defined) 3. Not objective 4. Not precise 5. Good definition

►A. Exercises 6. An empty set is any set. 1. Not clear (doesn’t comm. pt. ) 2. Not useful 3. Not objective 4. Not concise 5. Good definition

►A. Exercises 7. An atheist is like when some crazy nut denies that God exists. 1. Not clear 2. Not useful 3. Not objective (crazy nut) 4. Not concise (bad grammar) 5. Good definition

►A. Exercises 8. Love is unselfish concern for the best interests of another. 1. Not clear 2. Not useful 3. Not objective 4. Not concise 5. Good definition

►A. Exercises 9. A retable is a reredos. 1. Not clear 2. Not useful (reredos undefined) 3. Not objective 4. Not concise 5. Good definition

►A. Exercises 10. Braille is a system of writing and printing for blind people that consists of different patterns of raised dots that represent letters, 1. Notwords, clearnumbers, and punctuation. 2. Not useful 3. Not objective 4. Not concise (wordy) 5. Good definition

►A. Exercises Illustrate each idea. 11. point K

►A. Exercises Illustrate each idea. 13. line l

►A. Exercises Write a sentence describing each illustration. 15. n F

►A. Exercises Write a sentence describing each illustration. 17. Q l

■ Cumulative Review 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 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. 35. A = {x|x is a prime number greater than 2} B = {x|x is an even integer}

■ Cumulative Review 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. 36. A = {x|x is the square of an integer} B = {0, 1, 4, 9, 16, 25, . . . }

■ Cumulative Review 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. 37. A = {1, 11, 21, 31} B = {-11, 1, 121, 1331}

■ Cumulative Review 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. 38. A = {x|x > 2} B = {x|x ≤ 2}

Analytic Geometry Graphing Points

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

Cartesian plane II I origin III IV y x

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

Give the coordinate of each point. (-3, 3) B (5, 2) A x (0, -2) C y

Plot the following points. 1. (-1, 4) 2. (2, 2) 3. (0, -2) 4. (3, -2) 5. (3/2, 1) 1 2 5 3 y x 4