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Geometry Journal

Geometry Journal. Michelle Habie 9-3. Point, Line, Plane. Point: A mark or dot that indicates a location. Ex: Line: A straight collection of dots that go on forever. Ex: Plane: Flat surface that extends forever. Ex:. Collinear Points & Coplanar Points:. Collinear Points:

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Geometry Journal

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  1. Geometry Journal Michelle Habie 9-3

  2. Point, Line, Plane Point: A mark or dot that indicates a location. Ex: Line:A straight collection of dots that go on forever. Ex: Plane: Flat surface that extends forever. Ex:

  3. Collinear Points & Coplanar Points: Collinear Points: Points that are in the same line. Ex: Non collinear Points: Points that are not in the same line. Ex: Coplanar Points: Points that are on the same plane. Ex: Thisisanexampleofcoplanarpointsthat are notcollinear. This 3 points are coplanarandcollinear.

  4. Line, Segment, Ray Line: A straight collection of dots that go on forever. Ex: Segment: A line that has a beginning and an end. Ex: Ray: A line that has a starting point and in one side it keeps on going forever and in the other side, it stops. Ex: Thethreeofthemjointwopointshowever, some stop andothercontinuestheirpath.

  5. What is an intersection? Intersection: The point where a line crosses the x axis or the y axis. Passing across each other at exactly one point. Exmples: 1. 2. 3. Real LifeIntersection

  6. Postulate, Axiom, Theorem: Difference: Postulate: A statementthatisaccepted as truewithoutproof. Axiom: A statementthatisaccepted as truewithoutproof. Theorem: A statementthat has beenproven.

  7. RulerPostulate: Tomeasureanysegmentyou use a rulerandsubtractthevalues at the endpoints. Examples: 1. 2. 3. Use therulerpostulatetofindthedistancefromonepointtotheother. 5 8 A B Base 1 Base2

  8. SegmentAdditionPostulate: IfA,Band C are 3 collinearpointsand B isbetween A and C then AB+BC=AC. Examples: Use thispostulatetofindthedistantbetween 3 or more pointson a segment. A B C 1 2 3 Home Vista Hermosa Blvd. CAG

  9. Distancebetween 2 points: Tofindthedistancebetweentwopointsyou use thedistance formula: √(x2-x1)⌃2+(y2-y1)⌃2 Examples: 1. (2,4) (-1,0) D=√(2+1)⌃2+(4-0)⌃2= D=5 2. (3,-2) (6,-8) D=√(3-6)⌃2+(-2+8)⌃2= D=√45 3. (1,0) (-2,8) D=√(1=2)⌃2+(0-8)⌃2= D=√73

  10. Congruent–Equal: = Twothingsthathavethesamevalue. Wehaveto know thevalue ComparingValues AB=3.2 ≅ Twothingsthathaveequalmeasure. Mightnot know whatthevalueis. ComparingNames. --≅-- AB CD A, B are congruentandequal. While B, C are congruentbut, notequal. Examples: A B C

  11. PythagoreanTheorem: Thesumofthelegstothesquared has to be equaltothehipothenusetothesquare. Examples: a2+ b2=c2 If a=10 andb=12 Findc: c=√(102)+(122) C=√244 Find a A=√10⌃2-8⌃2 A=√100-64 A=√36=6 A=10 c=16 Findb b=√16⌃2-10⌃2 B=√256-100 = b=√156 B=8 c=10

  12. Anglesandtypesofangles: Anangleisthejoiningoftworayswith a commonpointcalledvertex. Wemeasuretheangles by thedistancefromraytoray, wemeasurethem in degrees. 1. Acuteangle (measures 0°-89°) 2. Rightangle (measuresexactly 90°) 3. Obtuseangle (measuresbetween 91°-179°) 4. Straightangle (measuresexactly 180°) Thepartsofanangle are itslegsandthevertex. Legs Interior Legs Vertex

  13. AngleadditionPostulate: Themeasurementoftwoincludedanglesisequaltothemeasurementofthewholeanglethatincludesboth. <CAD+<CAB=<BAD 1. m<CAD= 30° m<CAB=20° Findm<BAD m<BAD=30°+20°=50° 2. m<BAD= 75° andm<CAD= 15° Find m< CAB m<CAB=75°-15°=60° 3. <EIF=32°, <FIG=40°, <GIH=38° Findm<EIH m<EIH=32°+40°+38°=110° B C A D F E G H I

  14. Midpoint Themidpointisthepointthatbisects a segment in twocongruentparts. You can find a midpoint by measuringorusing a straightedge( compass). Examples: 1. F If EF= 10 and FG= 9, then F is NOT themidpointof EG. E G Theapple balances thisscalebecauseitrepresentsthemidpoint. A B C isthemidpoint Becauselies in themiddle ofsegmentA,C. 

  15. Angle Bisector: Itmeansto divide anangleintotwocongruentangles. Toconstructanangle bisector you use a compassand a rulertofindit. Example 1:

  16. Adjacent,Vertical, Linear PairsofAngles: Adjacent: Have a commonvertexsharing a raywith no common interior points. Vertical: Two non adjacentanglesform by twointersectinglines. Linear: Adjacentangleswith non commonsides are oppositerays.

  17. Supplementary& Complementary Angles: Supplementary: Anytwoanglesthatadd up to 180° Complementary: Anytwoanglesthatadd up to 90°

  18. AreaandPerimeterofShapes: A= s⌃ 2 P= 4s Example 1 : s=5in A=(5)⌃2=25in ⌃2 P=4×5=20in Example 2: s=3cm A=(3)⌃2=9cm⌃2 P=4×3=12 cm A= ½ lh L= a+b+c Example 1 : l= 5, w= 3, b=4, c=6 A = 5×3÷2= 7.5 u ⌃2 L = 5+4+6= 15u Example 2:l=7, w=4, b=2, c=5 A= 7×4÷2= 14u ⌃2 L=7+2+5= 14u A= lw P= 2l + 2w Example 1 : l= 2 cm, w= 1 cm A = 2×1=2cm ⌃2 P =2(2)+ 2(1)=6cm Example 2:l= 5 ft, w=3ft A= 5×3=15ft⌃2 P= 2(5)+ 2(3)= 16ft

  19. AreaandCircumferenceof a Circle Area= πr⌃2 Circumference: 2π r Example 1: r= 6 A(3.14)(6)⌃2 A=3.14×36 A=112.04u⌃2 Example 1: r= 8cm c= 2(3.14)(8) c= 50.24cm

  20. 5 StepProcess: Ifthreecansof soda cost $10.50. How muchwouldsevencansof soda cost? • Readitcarefully. • Understandtheproblem • Make a plan- I definetlyneedto set up a proportion. • 3 cans=7 cans ------ = ------ = 10.50 ×7 10.50 x ------------ 3 x=$24.50 5. Look Back iftheanswermakessense.

  21. Transformations: Rotate Reflect Translate Make a copyof a figure in a differentposition. A transformation can enlargeanobjectorshrinkanobject. Examples:

  22. Bibliography: • http://primaryhomeworkhelp.co.uk/time/pm.gif • http://gmat4all.com/diagrams/a1a.jpeg • http://www.bced.gov.bc.ca/irp/mathk7/icons/f6.gif • http://www.gogeometry.com/heron/angle_bisector.gif • http://content.tutorvista.com/maths/content/geometry/lines%20angles%20triangles/images/img61.gif • http://www.freemathhelp.com/images/lessons/angles5.gif • http://2000clicks.com/MathHelp/GeometryTheoremsLinearPair.gif • http://www.analyzemath.com/Geometry/angle_5.gif • http://www.gltech.org/library/April_geometry/supplementary2.gif • http://image.wistatutor.com/content/feed/tvcs/translation_0.jpg • http://image.wistatutor.com/content/feed/u1856/reflection.GIF • http://www.mathsisfun.com/geometry/images/rotation-2d.gif

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