1 / 18

G e o m e t r y J o u r n a l 2 By Michelle Habie

G e o m e t r y J o u r n a l 2 By Michelle Habie. Conditional Statement :. Conditional s tatement is formed by a hypothesis and a conclusion . It can be written in the form : If P then Q. Parts : If : hypothesis then : conclusion.

norman
Download Presentation

G e o m e t r y J o u r n a l 2 By Michelle Habie

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometry Journal 2 By Michelle Habie

  2. ConditionalStatement: Conditionalstatementisformed by a hypothesisand a conclusion. It can be written in theform: If P then Q. Parts: If: hypothesisthen: conclusion If I studygeometrythen I will pass the test. Iftheskyiscloudythenitwillraintoday. If I finish my homeworkthenI’mabletowatcht.v.

  3. Counterexample: isanexamplethatprovesthat a conjectureisfalse. CounterExample: No mammals can fly. A bat is a mammal. Threepoints are allwayscollinear. Threepoints lay onthesameplanebutonlytwoofthem are collinear. All prime numbers are odd.2 is a prime number.

  4. Definitionand Perpendicular Lines: Itis a conceptwritten in theformof a biconditionalstatementto describe a matematicalobject. Perpendicular lines are linesthatintersecteachotherforming a 90 degreeangle. A lineis perpendicular to a plane at a point. Thefloorof my housetothewalls. Theneedlesof a clockwhentheymatk 3 o’clock Thetrashholderisanexampleof a line perpendicular to a plane.

  5. Bi- ConditionalStatement: A biconditionalstatementis a statementthat can be written in theformof P ifandonlyif Q. They are usedtowritemathemathicaldefinitions. They are importantto use in ourmathematicallanguageandeverydaylife. Anangleisright IFF itmeasures 90 degrees. A triangleisacute IFF the 3 angles are acute. 3x+1=25 IFF 3=8

  6. DeductiveReasoning: Deductivereasoning uses logictofind a conclusionusingfacts. We use deductivereasoningtoapplythelawofdetachmentandthelawofsyllogism. Itisusedtorepresent a definitionusingsymbolsfor a betterunderstanding. Itworksmakingitsimplertounderstand. If I geton a dietthe I willlooseweight. IfI’m 18 yearsoldthen I willgetan ID. If I getan ID thenI’ll be ableto vote. Ifi’m 18 yearsoldthenI’ll be ableto vote. If I practicereadingthen my vocabularyskillswill be improven. SymbollicNotation: Itisusedtorepresent a definitionusingsymbolsfor a betterunderstanding. Itworksmakingitsimplertounderstand.

  7. LawsofLogic: LawofDetachment: Ifpqistrueandpistrueitfollowsthatqisalsotrue. LawofSyllogism: Ifpqandqr are trueitfollowsthat prisalsotrue. Examples: If I am 16 yearsoldthen I can get my driverslicense. If I have a blackberrythen I amabletochatwithpeoplewhohavebb.If I chatwithpeoplewithbbthen I willkeep in touchwith my friends. Iftwoanglemeasure 45° thenthey are congruent. Iftwoangles are congruentthentheymeasurethesame.

  8. AlgebraicProof: Analgebraicproofisanargumentthat uses logic, definitions, propertiesandprovenstatementstoprovethat a conclusionistrue. • 3x-2=7 Givenc. X=2 Given +2 +2 AdditionProp. ofEquality 4 MultiplicationPropofEquality 3x=9 DivisionProp. OfEqualityx=8 Simplify 3 3 Simplify x= 3 b. 3r= -12 Given 3 3 DiviionProp. OfEquality r=-4 Simplify

  9. SegmentProp. ofEquality TheSegmentAdditionPostulatestatesthatthesumofthepiecesthatmake up a segmentisthesame as thelengthofthewholesegment. Thesamepropertyworksforandanglethatisdividedintotwoor more parts. Thesumofallthepartsisthesame as thewholeangle. Home Vista Herm. CAG Examples: a c e AC+ CE= AE Home-CAG= Home-VH+ VH-CAG G-P= G-P+P-E+E-P Guate Palin Escuintla Puerto

  10. Two- columnProof: A two-columnproofiswrittenusingstatementsontheleftand a specificreasonforeachstatement in ordertofind a conclusiontoprovewhatisbeingaskedwith a process. Examples:

  11. SegmentPropertiesofCongruence: Reflexive: Segment AB isonlyequalto AB. (itself). Symmetric: No matter how wename a segmentitisequaltoitself. (AB=BA) Transitive: If AB=BC and BC=CD then AB=CD. Examples: Home-CAG=CAG-Home Home CAG C=l L=P then, C= P isthatthey are thesame in lengthorheight.(TransitiveProp). Laura’s BB= My BB My BB= Monica’s BB Laura’s= Monica’s BB Carlos Luis Pablo Laura Me Monica

  12. AnglePropertiesofCongruence: Reflexive: <BAC congruent <BAC. Symmetric: <BAC congruent <CAB. Transitive: If <XAW congruent <YAW , <YAW congruent <WAZ then <XAY congruent <WAZ. Examples: 1. 3. X <XYZ congruent <ZYX Y A D M A Z B E N 2. C O F B <ABC congruent <DEF ,<DEF congruent <MNO, and <ABC congruent <MNO. <ABC congruent <ABC C

  13. Linear PairPostulate: Itis made up oftwoadjacentanglesthatshare a rayand are supplementary. Examples: 1. 2. C ABC and CBD are linear pairthenx+ 60= 180° X= 120° X 60 A B D X+10+ 100= 180° X+110=180° X=180-110 X=70° B 3. A 100 X+10 ACB+ BCD= 180 ACB and BCD are linear pair. C D

  14. CongruentSupplementsTheorem: Iftwoangles are supplementsofthesameanglethenthetwoangles are congruent. Examples: 1. 2. <CBD is a supplementto <ABC and <YXZ isalso a supplementto <ABC SO, <CBD and <YXZ are congruent. Y C B A D X Z <1 issuppto <3 <2 issuppto <3 So, <1 iscongruentto <2. 110° 70° 70° <1 <2 <3

  15. <a <b 3. < c If <a issuppto <c Then <bisalsosuppto <c.

  16. Vertical Angles: Vertical angles are formedwhentwolines cross andtheoppositeangles are vertical andcongruent. In vertical anglesoppositeones (acrosseachother) measurethesame. Examples: If <a and <c are vertical then X-5 + 100 X= 100+5 X=105 X-5 2 <1 and <3 are vertical. a 3 1 a a 4 a 100

  17. X+16 X+16= 2x-6 16+6= 2x-x 22+x 2x-6

  18. Bibliography: http://3.bp.blogspot.com/_eIwxugTIJsw/SOUquUJShJI/AAAAAAAAATA/aLgWrMd6o3A/s400/3.3b.bmp http://www.utdanacenter.org/mathtoolkit/images/activities/geo_b3b_table.gif http://mrpilarski.files.wordpress.com/2009/09/proof-in-algebra-pilarski.jpg?w=417&h=333

More Related