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SECONDARY MATH II // MODULE 5
GEOMETRIC FIGURES – 5.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.2
Needhelp?Visitwww.rsgsupport.org
READY Topic:SymbolsinGeometryThroughoutthestudyofmathematics,youhaveencounteredmanysymbolsthathelpyouwritemathematicalsentencesandphraseswithoutusingwords.Symbolshelpthemathematiciancalculateefficientlyandcommunicateconcisely.Belowisasetofcommonmathematicalsymbols.Yourjobistomatchthemtotheirdefinitions.Arethesymbolslogical?
Symbol Definitions______1.= A.Absolutevalue–itisalwaysequaltothepositivevalueofthe
numberinsidethelines.Itrepresentsdistancefromzero.______2. B.Congruent–Figuresthatarethesamesizeandshapearesaidtobe
congruent.______3.
C.Parallel–usedbetweensegments,lines,rays,orplanes
______4.∆𝐴𝐵𝐶 D.LinesegmentwithendpointsGandH.Linesegmentscanbecongruenttoeachother.Youwouldnotsaytheywereequal.
______5.
E.RayGH–Theletterontheleftindicatestheendpointoftheray.
______6.
F.Usedwhencomparingnumbersofequalvalue.
______7. G.Plusorminus–indicates2values,thepositivevalueandthenegativevalue
______8.
H.TriangleABC
______9.
J.Indicatesthemeasureofanangle.Itwouldbesetequaltoanumber.
______10. K.Perpendicular-Lines,rays,segments,andplanescanallbeperpendicular
______11.
L.AngleABC–Themiddleletterisalwaysthevertexoftheangle.
______12.||
M.Similar–Figuresthathavebeendilatedaresimilar.
______13.
N.ThelengthofGH.Itwouldequalanumber.
______14.|𝑥| P.ReferstotheinfinitelineGH.Linesarenotequalorcongruenttootherlines.
m∠C
GH
⊥
∠ABC
GH
≅
GH
GH
±
READY, SET, GO! Name PeriodDate
SECONDARY MATH II // MODULE 5
GEOMETRIC FIGURES – 5.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.2
Needhelp?Visitwww.rsgsupport.org
SET Topic:Constructionofmidpoint,perpendicularbisector,andanglebisector,using“givens”tosolveproblems.Thefigureontherightdemonstratestheconstructionofaperpendicularbisectorofasegment.Usethediagramtoguideyouinconstructingtheperpendicularofthefollowinglinesegments.Marktherightanglewiththecorrectsymbolforrightangles.Indicatethesegmentsarecongruentbyusingslashmarks.
15.
16.
Thefigureontherightdemonstratestheconstructionofananglebisector.Usethediagramtoguideyouinconstructingtheanglebisectorofthefollowingangles.Markyourbisectedanglesascongruent.
17.
18.
19.
A B W
V
A
B
C
D
E
F G
H
I
SECONDARY MATH II // MODULE 5
GEOMETRIC FIGURES – 5.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.2
Needhelp?Visitwww.rsgsupport.org
Examinethediagramandaddanyinformationthatyouaregiven.Thinkhowyoucanusewhatyouhavebeengivenandwhatyouknowtoanswerthequestion.Planastrategyforfindingthevalueofx.Followyourplan.Justifyeachstep. 20.Given: 21.Given 22.Given:∆𝐵𝐸𝐶,∆𝐶𝐸𝐷, 𝑎𝑛𝑑 ∆𝐷𝐴𝐵arerighttriangles.
23.Given: bisects ,and .Find
Haveyouansweredthequestion?Thisproblemasksyoutodomorethanfindthevalueofx.
m∠C = 90º
m∠ABC = 90º
CF
∠ECD, m∠ECF = 2x +10m∠FCD = 3x −18 m∠FCE.
SECONDARY MATH II // MODULE 5
GEOMETRIC FIGURES – 5.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
5.2
Needhelp?Visitwww.rsgsupport.org
GO Topic:Translations,reflections,rotations
Performthefollowingtransformationsonthediagrambelow.24.LabelpointsC,E,Dwiththecorrectorderedpairs.25.Translate∆𝐶𝐸𝐷down4andright6.Labeltheimageas∆𝐶′𝐸′𝐷′andincludetheneworderedpairs.26.Draw𝐶𝐶′ ,𝐸𝐸′ , and 𝐷𝐷′ .Whatistheslopeofeachoftheselinesegments?27.Reflect∆𝐶𝐸𝐷acrossthex=0line.Labeltheimage∆𝐶!!𝐸!!𝐷!!.Includetheneworderedpairs.Draw𝐶𝐶′′ 𝑎𝑛𝑑 𝐸𝐸′′Whydidn’tyouneedtodraw𝐷𝐷′′?Whatistherelationshipbetween𝐶𝐶′′ and 𝐸𝐸′′tothe𝑥 = 0line?28.Rotate∆𝐶𝐸𝐷180ºaboutthepoint(-2,0).Labeltheimage∆𝐶′′′𝐸′′′𝐷′′′.
Includetheneworderedpairs.
ED
C