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Pablo Canga Geo Journal 2

Pablo Canga Geo 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.

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Pablo Canga Geo Journal 2

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  1. Pablo Canga GeoJournal 2

  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.

  3. Conditional (ifthen) Statements • A Conditionalstatementiswhen Q is true then p is true also. In otherwordsifthehypothesisis true thentheconclusionis true. If Q  P. • Ifyoufinishyourhomework, youmayplayoutside. • Ifyouhelp me withthework, I willpayyousomemoney. • Ifyoucleanthedog´scage, thenyoumaygotosleep.

  4. COUNTER EXAMPLES • Counterexamples are examplesthat show thatthehypothesisiswrong. Youjustneed 1 toproveitisnot true. • Ifyoujumptheramp, youwill die. Itisnot true becauseyou can land ok. • Ifyoudont do your HW nowyouwillget a 0. Not true becauseyou can do it in the bus. • Ifyoudon´twatch tv, youwontfinishyour chores. No becauseyou can stop watching in few minutes.

  5. Definitions • Definitions are theadjectivesorreasonsthat describe whysomethingisthatwayorwhatsomethingis. • Fireis a reactionthat has to do withenergy. • Tennisis a sport where a racketisused. • A t.v.attractsdiferenttypes of sygnals.

  6. BiconditionalStatement • TheBiconditionalstatementisknown as, If and onlyIf. In a shorterwayyouwriteit as Iff. Thissaysthat P if and onlyif Q. Thisislike a lawbecauseitwillonlygivethesameanswerallthe time. • Yougooutsideiffyou do yourhomework. • I willgotothemoviesiffitis Friday. • I willeat in Mc donaldsiff I have soccer practice.

  7. DeductiveReasoning • Thedeductivereasoningiswhenyouprovesomethingbylogicorobservations. Thisisnotthatsame as inductivemeaningthatyouprovesomethingbyfacts. • Allipodtouch are touch so thatmeansthatanyipodthatistouchisanipodtouch • Any animal that has furis a mamal so everymamal has fur. • Everyperiodis 75 minutes long, thereforifyou are in a perdiodthenitis 75 minutes.

  8. Laws of Logic • There are 2 laws. TheLaw of Detachmentthatsaysthatif p then q. P is true so then Q is true also. • Every Friday I gotothemovies. Today I wenttothemovies so todayis Friday. • EveryMonday I gotothegym. Today i am in thegym so todayisMonday. • Noteven 1 mamalputseggs. The animal I am lookinglayedanegg so itisnot a mamal.

  9. Theotherlawiscalledthelaw of syllogism. Thislawsaysthatif P then Q and if Q then R all are true. Thatmeansthat P then R is true too. • TodayisMonday. I am in themarket. EveryMonday I gotothemarket so Ifim in themarketthenitismonday. • Ifan animal eats bananas thenits a monkey. Thereisan animal eating bananas so itis a monkey. • Ifyouhave a longhairthentheywillcutit. They are cuttingyourhair so thatmeansyouhaveitlong.

  10. Linear PairPostulate LPP youknow me! The linear pairpostulatesaythatif 2 linesform 180 degreesthenthey are supplementary.

  11. AlgebraicProofs They are a series of stepsusedtoproveeachstepyou do toprovethegiven. Additive Substraction Multiplication Division And so…

  12. TwoCollumnProofs A waytoprove a statementwith a reason. Itisanorganized and fastwaytoprovethegiven and whatyouhavetoprove. http://3.bp.blogspot.com/_eIwxugTIJsw/SOUquUJShJI/AAAAAAAAATA/aLgWrMd6o3A/s400/3.3b.bmp

  13. CongruentComplement And Supplement Theorem Thecomplementary (congruent) theoremstatesthatif 2 ANGLES are congruent and form a rightanglethentheybothhavethesamemeasure, 90 degrees.

  14. Supplementary has thesame rule as beforewithcomplementary. Justthemeasurechangestothedoublewhichis 360 degrees,

  15. Vertical A ngleTheorem Thistheoremstatesthattheoppositeangles in a 360 angle are coungruent so theyhavethesamemeasure. Theother 2 vertical angles are alsocongruent.

  16. CommonSegmentTheorem • Thistheoremstatesthatif ab iscoungruenttocdthenaciscongruentalsotobd. Thisisused in segments. • My bathroomto my bedroomisthesamedistanceto my momsroom and herbathroom so thatmeansthat my bathroom and my momsbathroomisthesamedistancefrom my bedroomtoherbedroom. • DE isthesamedistancefrom FG so DF issamedistancecomparedtosegment EG. • My dogscage and my catscage has thesamedistanceto my birds and snakecage. So my dogs and birdsissamedistancetocats and snakescage

  17. I AM DONE

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