1.CircleAhasacenterat(-1,-1),andcircleBhasacenter(1,-2).

LoganperformstwotransformationsoncircleAtoshowthatcircleAissimilartocircleB.Oneofthetransformationsiscenteredat(-1,-1).Whatarethetransformations?(x,y)à(,)(x,y)à(,)

2.Inthediagramshown,chordsABandCDintersectatE.Themeasureof𝐴𝐶is120°, themeasureof𝐷𝐵is(2x) °,andthemeasureof∠𝐴𝐸𝐶is(4x) °.

Whatisthemeasureof∠𝐴𝐸𝐷?

3.TrapezoidABCDisinscribedincircleO.Diagonals𝐵𝐷and𝐴𝐶meetatpointEand𝐴𝐷isparallelto𝐵𝐶,asshown.

SelecttheanglesandvaluethatmakeatruestatementabouttrapezoidABCD.

4.CircleQhasaradiusrwithacentralangle∠AQBthatmeasuresx°,asshown.

A.Createanexpressionusingrandxthatcanbeusedtofindthelengthof𝐴𝐵,indegrees.B.Then,createanexpressionthatcouldbeusedtofindthelengthof𝐴𝐵,indegrees,ifcircleQweredilatedbyascalefactorof3.7.

5.Kyledefinesacircleas“thesetofallpointsequidistantfromagivenpoint.”ExplainwhyKyle’sdefinitionisnotpreciseenough.

6.TriangleSRTisshown.

Therearethreehighlightsintheparagraphthatshowequationsorphrasesthataremissing.Foreachhighlight,clickonthecorrectequationorphrase.Theverticesof∆𝑆𝑅𝑇areS(1,4),R(2,2),andT(1,3).Areflectionacrosstheline_______________Andthenacrosstheline_______________isthesameasatranslationof4unitstotherightand4unitsupbecausethelinesare_______________

7.RegularpentagonEFGHIwithcenterKisshown.

SelectallthetransformationsthatcarrypentagonEFGHIontoitself.

o areflectionacrosslineEK,a180°counterclockwiserotationaboutpointK,andareflectionacrossaverticallinethroughpointK

o a90°counterclockwiserotationaboutpointE,areflectionacrosslineFG,andaverticaltranslation

o areflectionacrosslineFI,areflectionacrosslineGH,anda180°clockwiserotationaboutpointK

o areflectionacrossaverticallinethroughpointK,a180°clockwiserotationaboutpointK,anda

reflectionacrosslineEK

o a180°clockwiserotationaboutpointE,areflectionacrossaverticallinethroughpointE,andareflectionacrossahorizontallinethroughpointE

8.EvelynisdesigningapatternforaquiltusingpolygonEQFRGSHPshown.

EvelyntransformsEQFRGSHPsothattheimageofEisat(2,0)andtheimageofRisat(6,-7).WhichtransformationcouldEvelynhaveusedtoshowEQFRGSHPanditsimagearecongruent?A.EQFRGSHPwasreflectedovertheliney=x+2.B.EQFRGSHPwastranslatedright7unitsanddown4units.C.EQFRGSHPwasrotated135degreesclockwiseaboutthepointQ.D.EQFRGSHPwasrotated90degreesclockwiseaboutthepoint(-3,-1).

9.Mrs.Henrygaveherstudentsanincompleteproofasshown.Given: 𝐻𝑄 ∥ 𝑇𝑋 ∠𝐹𝑁𝐻 ≅ ∠𝑁𝑃𝑅Prove: ∠𝑅𝑉𝑊 ≅ ∠𝑋𝑊𝑍Completetheproofbydraggingthecorrectreasonstothetableforlines3and6.

10.Afigureisshown,where𝐷𝐸isparallelto𝐵𝐶.Given: 𝐷𝐸 ∥ 𝐵𝐶Prove: ∠𝐴𝐵𝐶 + ∠𝐵𝐶𝐴 + ∠𝐶𝐴𝐵 = 180°Dragstatementsfromthestatementscolumnandreasonsfromthereasonscolumntotheircorrectlocationtocompletetheproof.

11.Aproofwithsomemissingstatementsandreasonsisshown.Given: PQRSisaparallelogram. 𝑃𝑄 ≅ 𝑄𝑅Prove: PQRSisarhombus.

Dragthecorrectstatementfromthestatementscolumnandthecorrectreasonfromthereasonscolumntothetabletocompleteline3oftheproof.

12.Rubencarriesoutaconstructionusing∆𝐴𝐵𝐶.Clicktheplaybuttontoseeapartofhisconstruction.WhatwillbetheresultofReuben’sconstruction?

A. Rubenconstructsasegmentperpendicularto𝐴𝐶.

B. Rubenconstructsthebisectorof𝐴𝐶.

C. Rubenconstructsananglecongruentto∠𝐵.

D. Rubenconstructsthebisectorof∠𝐵.

13.AlejandrocutacirclewithcircumferenceCandradiusrinto8congruentsectorsandusedthemtomakethefigureshown.Alejandronoticedthatthefigurewasveryclosetotheshapeofaparallelogram.Selectallthestatementsthatapplytothefigure.

o Theheightoftheparallelogramisapproximatelyequaltothecircle’sdiameter.

o Theareaoftheparallelogramisapproximately!!Cr.

o Thelengthoftheparallelogramisapproximatelyequaltothecircle’scircumference.

o Theradiusofthecircleisapproximatelyequaltotheheightoftheparallelogram.

o Theareaoftheparallelogramisapproximately8( !"

!"#𝜋𝑟!).

14.Asphosphateismined,itmovesalongaconveyorbelt,fallingoffoftheendofthebeltintotheshapeofarightcircularcone,asshown.

Ashorterconveyorbeltalsohasphosphatefallingoffoftheendintotheshapeofarightcircularcone.Theheightofthesecondpileofphosphateis3.6feetshorterthantheheightofthefirst.Thevolumeofbothpilesisthesame.Tothenearesttenthofafoot,whatisthediameterofthesecondpileofphosphate?

15.Arectangleandahorizontallinesegmentareshown.

Whatistheresultingobjectwhentherectangleisrotatedaroundthehorizontallinesegment?A.B.C.D.

16.Johnnywantstofindtheequationofacirclewithcenter(3,-4)andaradiusof7.Heusestheargumentshown.Therearethreehighlightsintheargumenttoshowmissingwordsorphrases.Foreachhighlight,clickonthewordorphrasethatcorrectlyfillsintheblank.Johnny’sArgumentLet(x,y)beanypointonthecircle.Then,thehorizontaldistancefrom(x,y)tothecenteris_______________.Theverticaldistancefrom(x,y)tothecenteris_______________.Thetotaldistancefrom(x,y)tothecenteristheradiusofthecircle,7.The_______________cannowbeusedtocreateanequationthatshowstherelationshipbetweenthehorizontal,vertical,andtotaldistanceof(x,y)tothecenterofthecircle.

17.OnediagonalofsquareEFGHisshownonthecoordinategrid.

Therearetwohighlightsinthesentencetoshowwhichwordorphrasemaybeincorrect.Foreachhighlight,clickthewordorphrasethatiscorrect.ThelocationofpointFcouldbe_______________becausediagonalsofasquarearecongruentand_______________.

18.TheequationforlineAisshown.

𝑦 = −23 𝑥 − 4

LineAandlineBareperpendicular,andthepoint(-2,1)liesonlineB.WriteanequationforlineB.

19.PointsA,B,andCarecollinearandAB:BC=!!.PointAislocatedat(-3,6),pointBislocatedat(n,q),

andpointCislocatedat(-3,-4).Whatarethevaluesofnandq?

20.PolygonABCDEisshownonthecoordinategrid.

Whatistheperimeter,tothenearesthundredthofaunit,ofPolygonABCDE?

21.Matcheachbuildingwiththegeometricshapesthatcanbeusedtomodelit.

22.ThepopulationofFloridain2010was18,801,310andthelandareawas53,625squaremiles.Thepopulationincreased5.8%by2014.A.Tothenearestwholenumber,whatisthepopulationdensity,inpeoplepersquaremile,forFloridain2014?B.Tothenearestwholenumber,howmuchdidthepopulationdensity,inpeoplepersquaremile,increasefrom2010to2014?

23.Thetrunkofapalmtreehascylindricaltubesthatcarrywater.Eachtubeis0.0003meterswide.Oneofthetubesinapalmtreetrunkisshown.

A.Usingthediagramasamodel,approximatelyhowmanytubescouldfitinapalmtreetrunkwithadiameterof0.5meters?B.Thetubesinapalmtreearebetween20to21meterslong.Whatistheapproximatevolume,incubicmeters,ofonetube?

24.QuadrilateralMATHisshown.

QuadrilateralMATHisdilatedbyascalefactorof2.5centeredat(1,1)tocreatequadrilateralM’A’T’H’.Selectallthestatementsthataretrueaboutthedilation.

o 𝑀𝐴 ≅ 𝑀′𝐴′

o 𝐴′𝑇′willoverlap𝐴𝑇.

o 𝑀′𝐴′willoverlap𝑀𝐴.

o Theslopeof𝐻𝑇isequaltotheslopeof𝐻′𝑇′.

o Theareaof𝑀′𝐴′𝑇′𝐻′isequalto2.5timestheareaofMATH.

25.TriangleRTVisshownonthegraph.

Triangle R’T’V’ is formed using the transformation (0.2x, 0.2y) centered at (0, 0). Select the three equations that show the correct relationship between the two triangles based on the transformation.

o 𝑅𝑉 = 5𝑅′𝑉′

o !!!!!"

= !"!.! !"

o 0.04 10𝑅𝑇 = 10𝑅′𝑇′

o 𝑅𝑇 = 0.2𝑅′𝑇′

o 0.2𝑇′𝑉′ = 𝑇𝑉

o !"!!!!

= !"!.! !"

26. Katherine uses ∆𝐴𝐵𝐶, where 𝐷𝐸 ∥ 𝐴𝐶 to prove that a line parallel to one side of a triangle divides the other two sides proportionally. A part of her proof is shown.

Which statement completes step 8 of the proof?

A. 𝐵𝐴 − 𝐵𝐷 = 𝐷𝐴 and 𝐵𝐶 − 𝐵𝐸 = 𝐸𝐶

B. 𝐴𝐷 = 𝐵𝐷 and 𝐶𝐸 = 𝐵𝐸

C. !"!"= !"

!"

D. !"

!"= !"

!"

27. Gabriel wrote a partial narrative proof to prove 𝐹𝐷 ≅ 𝐵𝐷. Given: 𝐴𝐷 bisects ∠𝐸𝐴𝐶 ∠𝐹𝐷𝐴 ≅ ∠𝐵𝐷𝐴 Prove: 𝐹𝐷 ≅ 𝐵𝐷 There are three highlights in the paragraph to show blanks in the proof. For each highlight, click on the word or phrase to fill in the blank. It is given that 𝐴𝐷 bisects ∠𝐸𝐴𝐶, and ∠𝐹𝐷𝐴 ≅ ∠𝐵𝐷𝐴. Since 𝐴𝐷 bisects ∠𝐸𝐴𝐶, then ∠𝐷𝐴𝐸 ≅ ∠𝐷𝐴𝐶 from the definition of angle bisector. 𝐴𝐷 ≅ 𝐴𝐷 by the reflexive property. ∆_______________≅∆_______________becauseof_______________.Therefore,𝐹𝐷 ≅ 𝐵𝐷becausecorrespondingpartsofcongruenttrianglesarecongruent.

28. The learning Tower of Pisa is 56.84 meters (m) long.

In the 1990s, engineers restored the building so that angle y changed from 5.5° to 3.99°. To the nearest hundredth of a meter, how much did the restoration change the height of the Leaning Tower of Pisa?