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Geo 2 Chavez

on Mar 22, 2011

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Brief Geo lesson

Brief Geo lesson

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Geo 2 ChavezPresentation Transcript

• Journal 2 ___(0-10 pts) Describe what a conditional if-then statement and the different parts of a conditional statement. Give at least 3 examples. √ ___(0-10 pts) Describe what a counter-example is. Give at least 3 examples. √ ___(0-10 pts) Describe what a definition is. Give at least 3 examples. √ ___(0-10 pts) Describe what a bi-conditional statement is. How are they used? Why are they important? Give at least 3 examples. √ ___(0-10 pts) Describe what deductive reasoning is and how it is used. Include a discussion about symbolic notation and how it works. Give at least 3 examples. √ ___(0-10 pts) Describe the laws of logic. Give at least 3 examples of each. √ ___(0-10 pts) Describe how to do and algebraic proof using the algebraic properties of equality. Give at least 3 examples. ___(0-10 pts) Describe the segment and angle properties of equality and congruence. Give at least 3 examples. ___(0-10 pts) Describe how to write a two-column proof. Give at least 3 examples. ___(0-10 pts) Describe the linear pair postulate. Give at least 3 examples. ___(0-10 pts) Describe the congruent complements and supplements theorems. Give at least 3 examples of each. ___(0-10 pts) Describe the vertical angles theorem. Give at least 3 examples. ___(0-10 pts) Describe the common segments theorem. Give at least 3 examples. ___(0-5 pts) Neatness and originality bonus ____Total points earned Jose Andres Chavez
• Describe what a conditional if-then statement and the different parts of a conditional statement. Give at least 3 examples.
• The conditional if-then statement is a statement in which you confirm your hypothesis or P with an if then Q.
• Examples
• If im going to the beach then it is Semana Santa
• If the dog barks then there is an intruder
• If going to school then I want to go to College.
• Describe what a counter-example is. Give at least 3 examples.
• The counter example is the one single example that proves a conjencture wrong.
• Examples
• A number divided by 5 is divisible by 10 and will always be a whole number. Counter Ex: 35/5=7 35/10=3.5
• All NBA players are over 2,00m high. Counter ex: Rajon Rondo of the Boston Celtics is 1,83m high.
• Only the Lakers and the Celtics have won the NBA title more than 3 times. Counter Ex: The San Antonio Spurs and the Chicago Bulls have won the NBA title 4 and 6 times respectibly.
• Describe what a definition is. Give at least 3 examples.
• Definitions are statements that describe a Mathemathical term and they can be applied to biconditional statements.
• Examples
• An angle is only a right angle iff it is 90*.
• An angle is only a commplementary angle if both angles add up to 90*
• An adjacent angle is only adjacent iff its composed of two angles that share a common endpoint
• Describe what a bi-conditional statement is. How are they used? Why are they important? Give at least 3 examples .
• A biconditional statement is a statement in which the conditional and converse are both true. They are stated with the iff or  . They are important because they are really usefull for proving the statement in a firm way. Examples
• A linear pair is a linear pair iff it adds up to 180* with two adjacent angles who are opposite rays.
• An animal is a member of the feline family iff he is a cat.
• A phone is a phone iff it can receive and make calls.
• Describe what deductive reasoning is and how it is used. Include a discussion about symbolic notation and how it works. Give at least 3 examples
• Deductive reasoning is the procedure of collecting information to take a decision or an opinion based on facts. The steps are the following. 1. Collect data,2. Look at all the facts,3. Use logic to make a conclusion.
• Examples: Determine whether or not if its Deductive or Inductive Reasoning:
• If you are going to the concert, You must have tickets. You have tickets Conjecture You want to go to the concert. Inductive reasoning: Theres is no given fact you want to go maybe they forced you to go
• Describe the laws of logic. Give at least 3 examples of each.
• The laws of logic are the following.
• The Law of Detachment which is If P  Q is true then we should assume if P is true then we must assume Q is also true.Examples
• If I have tickets , I am going to the concert. So If I am going to the concert, I have tickets.
• If the dog runs, then he is excersicing. So if the dog is excersicing, then the dog is running.
• If I have free time, I play Call of Duty. So if I am playing Call of Duty, I have free time
• The Law of Syllogism is the following If P-  Q is true and Q  R is true then if P is true R must be true. Examples
• If theres no signal,then theres no internet. If theres no internet I cant go to Facebook. So if theres no signal I cant login to Facebook.
• If theres no food, then I cant eat. If I cant eat then I am fatigued. So If thers no food, I am fatigued.
• If I have no money, then I am poor. If I am poor then I cant buy anything. So If I have no money, I cant buy anything.
• Describe how to do and algebraic proof using the algebraic properties of equality. Give at least 3 examples.
• Algebraic proofs are just like a normal proof. The main goal is to prove something in this case an algebraic equation. The steps are easy you make a table and solve the problem step by step describing your actions.
• Example
• -6= 4x +2 Given 3y +3 = 18 Given 7y -14=0 Given
• -2 -2 Subtraction Prop -3 -3 Substaction Prop +14 +14 Adding Prop
• -8=4x Simplify 3y= 15 Simplify 7y=14 Simplify
• /4 /4 Division Prop /3 /3 Division Prop /7 /7 Division Prop
• -2=x Simplify Y=5 Symmetric Prop Y=2 Symmetric Prop
• X=-2 Symmetric Prop
• Describe the segment and angle properties of equality and congruence. Give at least 3 examples.
• Ok the equality and congruent properties are easy and usefull they are the following:
• Properties of Equality
• Addition Property: If A=b then a+c=b+c
• Subtraction Property : If a=b then a-c=b-c
• Multiplication Prop : If a=b then ac=bc
• Division Prop: If a=b and c≠0 then a/c =b/c
• Reflexive Prop: a=a
• Symmetric Prop: if a =b then b=a
• Transitive Prop: If a=b and b=c then a=c
• Substitution Prop: If a=b then b can be substituted for “ a”
• Properties Of Congruence :
• Reflexive Prop: figure A is congruent to figure A (like a mirror)
• Symmetric Prop: If figure A is congruent figure B, the figure B is congruent figure A
• Transitive Prop: If figure A is congruent to figure B and Figure B is congruent to figure C then Figure A congruent to figure C
• Examples: Reflexive prop of equality 3x=3x, Transitive prop of equality Angle A= Angle B, Angle B= Angle C so Angle A is = to Angle C, Substractive prop pf Equality If 3x=5 then 3x – 2 = 5-2
• Describe how to write a two-column proof. Give at least 3 examples.
• How to write a two collum proof. Two collum proofs are easy to write them you need the information GIVEN to start defragmentating the information and organaizing it in the chart which goes with Reason and Statement. Reason being the property it follows and statement is what’s left as we defragment it.
• EXAMPLES
• Statement | Reason Statement | Reason
• 2x-6=4x-10 |Given TU congruent UV |Given
• +10 +10 |Addition Prop UT + UV = SV |Def of congruent Seg.
• 2x + 4 =4x |Simplify UT + SV= UV |Seg Add Post.
• -2x -2x |Sub. Prop SU+TU=SV |Congruent
• 4 = 2x | Simplify
• /2 /2 |Division Prop.
• 2= X |Symmetric Pr.
Statement | Reason 3x-8=19 | Given +8 +8 | Addition Prop 3x=27 | Simplify 3 3 | Division Prop X= 9 | Simplify
• Describe the linear pair postulate. Give at least 3 examples.
• LPP: or the linear pair postulate states that all linear pairs are supplementary to each other.
180* 180* 180*
• Describe the congruent complements and supplements theorems. Give at least 3 examples of each.
• Both theorems talk about how angles either complement or supplement each other
• Congruent Supplements: This states that If two angles are supplementary to the same angle then the two angles are congruent.
• Congurent Complements: This states that If two angles are complementary to the same angle then the two angles are congruent.
• EXAMPLES:
• Complementary
• Supplementary
• Describe the vertical angles theorem. Give at least 3 examples.
• The vertical angles theorem states that Vertical angles are congruent.
• Examples
1 2 3
• Describe the common segments theorem. Give at least 3 examples.
• This theorem states that collinear segments are congruent to each other.
• Examples
X Y W Z Wx congruent to YZ or WY congruent to XZ 1 2 3 4 A B C D 1,2 collinear to 3,4 or 1,3 collinear to 2,4 AB collinear to CD or BD collinear to AC
• THANKS. I HOPE YOU LEARNED