secondary math ii // module 5 geometric figures...

SECONDARY MATH II // MODULE 5

GEOMETRIC FIGURES – 5.2

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5.2

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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

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mathematicsvisionproject.org

5.2

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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

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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

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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