Logic & Compound Statement
⢠Logic
âis the study of how people think & reason correctly
Determine whether if the sentence is a Statement or not.
a.Did you eat today?
b. Sir. Layague is the best teacher. No,becausethisisa question
⢠Statement -is a declarative sentence that can either be true or false.
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Conjecture
-an educated guess based in data or examples.
InductiveReasoning is when someone makes observations then makes a general conclution. may also not lead you to the right conclution.
DeductiveReasoning
Is a general conclution to a particular reasoning
If conclution is correct then the statement is correct
InductiveReasoning DeductiveReasoning Every swan you have seen is white, therefore all swans are white. All human are mortals, socrates is human. Therefore socrates is a mortal.
Syllogism
a type of deductive reasoning where it consists a major and a minor premise and a conclusion.
Complete each syllogism! generalstatement(a),a particularstatement(b),and conclusion(c).
1. a : All dogs are mamals. b : My pet is a dog . c :
z:Therefore,mypetisa mammal.
2. a : All human are mortals b : c : Therefore socrates is a mortal.
b:Socratesisahuman. Negation the opposite of the given mathematical statement. The symbol to indicateh negation is
If-then Statement
Converse Statement Is done by switching the hypothesis and conclution
Writetheconverseofthe statement.
If you dont have any contribution, then you will have seperate PB :ifyouhaveaseperate Pb,thenyoudonthave anycontribution. Inverse Statement Is done by negating the hypothesis and conclution
Conditional Statement
Alsoknownasif-thenstatement The âifâisthehypothsisandâthenâisthe conclution,andisnotalwaysinaifthenform
TruthValueof Conditional Statement
Identifythehypothesis
A.Ifyoustudywell,thenyou willpasstheexam. Submit
Youwillpasstheexam Youstudywell
Identifytheconclution. B.Youwontbesleepy,ifyou sleptearly.
Youwontbesleepy
Yousleptearly
Writetheinverseofthe statement.
If you dont have any contribution, then you will have seperate PB :ifyoudonothavea seperatePb,thenyoudo nothaveany contribution.
Contrapositive Statement Is made by switching and negating hypothesis and the conclution.
Biconditional Statement Is a compound statement thats true if and only if they both have the same value.
Writethecontrapositive ofthestatement Ifyoudonthaveany contribution,thenyouwill haveseperatePB. : if you do not have a seperate Pb, then you do not have any contribution.
TruthValueof BiconditionalStatement
Symbols
Given Statemen
1) If a polygon is a quadrilat eral, then it has four sides.
2) If a number is multiplie d by 1, then the result is the number.
Introductionto Congruent Triangles
Corresponding sides:
Corresponding sides:
Corresponding angles:
Correspondingparts
Partsthatappearinidenticalshapesintwo similarshapes
Correspondingsides
Aretwomatchingsidesinthesamespot butindifferentshapes
Correspondingangles
Aretwomatchinganglesinthesamespot butindifferentshapes
Correspondingangles
Aretwomatchingverticesinthesamespot butindifferentshapes
Congruence
Corresponding angles:
Referstothesameshape&sizeandhavingthe samemeasure
Congruenttriangles
trianglesthathavethesameshape&sizeandthe samemeasure.
CPCTC
CorrespondingPartsofCongruentTrianglesare Congruent
Provingtriangle congruence.
Postulate
SSSCongruence
Postulate
Ifthreesidesofonetriangleare congruenttothecorrespondingsidesof theothertriangle,thenbothtrianglesare congruent.
IncludedAngle
Is an angle between two sides
SASCongruence
Postulate
If two sides and the included angle of one triangle are congruent to the other two sides of the other triangle and the included angle of another triangle, then the two triangles are congruent.
Ex.
included side
is the side which endpoints are the vertices of the two given angles.
ASACongruence
Postulate
- If two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the two triangles are congruent
Theorem
If two angles and a non-included side of one triangle are congruent to two angles and non-included side of another triangle, then the two triangles are congruent.
SolvingCorresponding
PartsofCongruent triangles
Solve for x and find XZ.
1 Solve for X
12x + 11 = 11x + 13 12x - 11x = 13 - 11 x = 2
Solution : The two angles are congruent by ASA Postulate, therefore by CPCTC, the sides are congruent.
2 Find XZ XZ = 11x + 13 XZ = 11(2) + 13 XZ = 22 + 13 XZ = 35
Solve for x and find the measure of angle C.
Solution : The two angles are congruent by SSS Postulate, therefore by CPCTC, the angles are congruent.
1 5x - 20 = 3x + 14 5x - 3x = 14 + 20 2x = 34 x = 17
Solve for x and find the measure of angle O.
Solution : The two angles are congruent by SAA Postulate, therefore by CPCTC, the angles are congruent 1
Solve for x
8x = 4x + 24 8x - 4x = 24 4x = 24 x = 6
2 Find the measure of angle O. mâ O = 8x mâ O = 8(6) mâ O =
Parallellines cutbya transversal
Parallel lines
Arelinesthatdo notintersect
Coplanar lines arelineslyingon thesameplane.
Perpendicular Lines
are lines that intersect at right angles.
Corresponding
Angles
a pair of interior and exterior angles on the same side of a transversal that do not form a linear pair.
Alternate interiorangles a pair of interior angles on opposite sides of a transversal that do not form a linear pair
Intersecting Lines arelinesthathave acommonpoint.
Transversal lines is a line intersecting two or more lines.
Alternate exteriorangles
apairofexterioranglesonopposite sidesofatransversalthatdonotforma linearpair.
3andâ 5
4andâ 6 Corresponding AnglesPostulate (PCACPostulate)
Iftwoparallellinesarecutbya transversal,thencorrespondingangles arecongruent.
Redisthetransversal blueistheparallellines
thealternateinterioranglesare congruentbecausethe2parallel lines(m||n)arecutbya transversal(â t)thatswhyâ eand â carecongruent
Iftwoparallellinesare cutbyatransversal,then alternateexteriorangles arecongruent.
1and
8
Sameside interiorangles interioranglesonthesamesideofa transversal.
Redisthetransversal blueistheparallellines
thecorrespondinganglesare congruentbecausethe2parallel lines(m||n)arecutbya transversal(â t)thatswhyâ band â farecongruent
Iftwoparallellinesarecutbya transversal,thenalternateinterior anglesarecongruent.
thealternateexterioranglesare congruentbecausethe2parallel lines(m||n)arecutbya transversal(â t)thatswhyâ aand â garecongruent
If two parallel lines are cut by a transversal, then same-side interior angles are supplementary
Namepairsofanglesasindicated.
a)alternateinteriorangles
Answer:
b)alternateexteriorangles
thesame-sideinterior anglesaresupplementary becausethe2parallel lines(m||n)arecutbya transversal(â t)thatswhy â candâ fare supplementary Redisthetransversal blueistheparallellines
c)correspondingangles
Answer:â 2andâ 6 â 1andâ 5 â 3andâ 7
d)samesideinteriorangles
Answer:â 3andâ 6
4andâ 5
Probability
Is the chance that something will happen, like events cannot be predicted with total certainty.
Probability experiment Is a chance process that leads to a well defined result of an outcome.
Outcome
Is the result of the first try of an experiment
EXPERIMENT Outcome
rolling a die
1, 2, 3, 4, 5, 6
Flipping a coin Heads or tails
Sample space
is a set of all possible outcomes or sample points and is denoted by the letter âSâ.
Sample point is one of the possible outcomes.
Point rolling a die 1, 2, 3, 4, 5, 6
Flipping a coin Heads or tails tails
Event is a set of one or more outcomes that has to contain the given conditions
Getting an odd number when rolling a die Getting Tails 3 times when flipping a coin
Unable
Composed by sofia
In a world of people left and right I chose you, we may not intersect But were still close. Every path you made i followed secretly I wanted to be with but i couldnt I wanted to intersect with you until infinity But with this cruel world i cant. I admired you from afar, everday longing for you. Every eye contact, waves good bye laughing together i cherished.
Were a pair that had a lot in common same music taste, fav foods, hobbies however weâll soon drift apart with time.
C o m i c s
