Chapter 2 Test

What is a plane formed by?

Three noncollinear points

Are vertical angles congruent?

Yes

Truth Table-positives

1) If p and q are true, then p-->q is true 2) If p is true but q is false then p-> is false 3) If p is false but q is true then p>q is true 4) if p is false and q is false then p->q is true

Truth table-opposites/negatives

1) if ~p and ~q is false, then ~p->~q is true 2) if ~p is false and ~q is true, then false 3) If ~p is true and ~q is false, then true 4) If ~p is true and ~q is true, then true

Find X:linear pair m<1: x+10 m<2: 3x+18

1. 4x+28=180 2. Subtract: 28-4x=180 3. Division: 152/4=x is 38

Find x: complmetary pair m<4: 2x-5 m<5: 4x-13

1. 6x-18=90: Substitution POE 2. Add 18 to 90: Addition 3. 6x=108: Division 4. x=18

Find x: vertical angles m<6: 7x-24 m<7: 5x+14 how is solving for these angles different?

1. 7x-24=5x+14: given 2. 2x=-38: Subtraction and addition POE 3. x=-19: Division POE 4. Solving for vertical angles if different because you do not know their sum mass, but only the fact that they equal each other

Grayson to Apex is the same distance as Redding to Pine Bluff. Prove that the distance from Grayson to Redding is the same distance from Apex to pine bluff(statement table)

1. AR=AR: Reflexive 2. GA+AR=RP+AR: Addition property 3. GA+AR=GR, RP+AR=AP: Segment addition 4. GR=AP: Substitution

Use statement proof to solve: AB=DE, B is midpoint of AC and E is midpoint DF Prove: BC=EF

1. State the given 2. AB=BC: midpoint formula DE=EF 3. BC=EF

Use statement proof to solve: <1 and <2 form a linear pair; <2 and <3 are supplementary Prove: <1=<3

1. m<1+m<2=180 m<2+m<3=180: Given 2. <1+<2+<2=<3 cancel out 2s: Subtraction POE 3. <1=<3

Solve angle relationships: <9 and <10 is complementary, <7 and <8 are complementary. <7=<9, m<8=41

41=m<8 90-41=49: m<7 m<7 and m<9=49 m<10=41 Theorem 2.10

Define adjacent and linear pair

Adjacent=sharing a common side and vertex Linear pair=two angles w sum measure of 180

Example of inductive reasoning

Ben's mother orders pizza every Friday

Example of law of syllogism Given=If an animal is a red wolf, then its scientific name is Canis rufus. If an animal is named Canis rufus, then it is endangered

Conclusion: If an animal is a red wolf, then it is endangered

Example of law of detachment Given: If a car is out of gas, then it will not start. Sarah's car is out of gas

Conclusion: Sarah's car will not start

Converse, inverse and contrapositive

Converse=q-->p Inverse=~p-->~q Contra=~q-->~p

What do we use to validate conclusions?

Deductive reasoning

The financial formula for simple interest is I=prt I=Interest P=principle R=rate T=time Solve formula for r

Divide the entire equation by pt; r=1

If <1 and <2 are adjacent angles then <1 and <2 form a linear pair?

False, they can be congruent

What should I focus on when finding the value of x with vertical angles?

Get rid of one of the x values

Claim Paragraph proof: E is the midpoint of AB and CD, AB=CD. Write proof that AE=ED

Half of AB=AE and half of CD=CE. Since AE is half of AB and CE is half of CD, AE=ED

Law of Detachment

If p --> q is a true statement and p is true, then q is true

Law of Syllogism

If p-->q and q-->r are true statements, then p-->r is a true statement.

Name the postulate: Lines L and M intersect at point Q

Intersecting Lines Postulate: When two lines intersect it will always be at a point

Name the postulate: Planes J and K intersect at line m

Intersecting Planes Postulate: when two planes intersect it will always be on a line

What is the definition of proof?

Logical argument in which each statement you make is supported by a statement that is accepted as true

deductive reasoning

Reasoning that uses rules, postulates, facts and other given information to make conclusions Ex.=If 3x+5=11 then x=2

If QA=QA, which property would justify it?

Reflexive

If BC=DE was converted to BC=EF in a statement proof table, which property would justify it?

Substitution, NOT TRANSITIVE

If AB=CD, and then was switched to CD=AB, which property would justify it?

Symmetric

If AB=BC and BC=CE, then AB=CE

Transitive property

If line GH and JK form a right angle and intersect at P, then GH=JK

True

TOF: A plain contains at least three lines

True: Planes postulate

Valid or not: If a point is the midpoint of a segment, it divides the segment into two congruent segments. R is the midpoint of QS

Valid: Definition of midpoints

quadrilateral

a four-sided shape(noncollinear points)

Inductive reasoning

reasoning based on patterns you observe, using logic

Conditional statement

statement that can be written in if-then form

TOF: negative plus a negative is always negative

true