55. Determining Scale using Coordinate Points...
Transcript of 55. Determining Scale using Coordinate Points...
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DeterminingScaleusingCoordinatePointsScaleisdeterminedbycomparinganimage(thenewfigure)toitspre-image(theoriginalfigure)usingafraction.Basically,𝑠𝑐𝑎𝑙𝑒 = !"#
!"#.Thisformulaapplieswhetheryouareusingsidelengthsorx-ypoints.Remember,theprime
symbol(‘)isusedtoidentifytheimage(newfigure).
Example:Determinethescalefactorofthedilatedfigureusingthegivenpoints.𝑋(20, 36), 𝑌(8, 28), 𝑍(20, 16),𝑋′ 5, 9 ,𝑌′ 2, 7 & 𝑍′ 5, 4 Sincetheproblemusestheterm“dilatedfigure,”youknowthatthefiguresaresimilar(whichmeansyoudonotneedto
checkthescale).Pickanypointanditsmatchtocreatethescale.New:𝑋′ 5, 9 Old:𝑋 20, 36
𝑆𝑐𝑎𝑙𝑒 =𝑋!
𝑋=
(5, 9)(20, 36)
𝑆𝑝𝑙𝑖𝑡 𝑢𝑝: 520
& 936
𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦: 5 ÷ 520 ÷ 5
=14
& 9 ÷ 936 ÷ 9
=14
Thescalefactoris!!.
Determinethescalefactorofeachdilatedfigureusingthegivenpoints.1.𝐴 2, 4 & 𝐴′(5, 10) 2.𝐵 5, 10 & 𝐵′(2, 4) 3.𝐶! 6, 15 & 𝐶(8, 20)
4.𝐷! 8, 20 & 𝐷(6, 15) 5.𝐸 12, 18 & 𝐸′(28, 42) 6.𝐹! 12, 18 & 𝐹(28, 42)
7.𝐺! 2, 10 ,𝐻! 16, 6 , 𝐼! 4, 18 , 𝐺 9, 45 ,𝐻 72, 27 & 𝐼(18, 81)
8.𝐺 2, 10 ,𝐻 16, 6 , 𝐼 4, 18 , 𝐺′ 9, 45 ,𝐻′ 72, 27 & 𝐼′(18, 81)
9.𝑀! 36, 44 ,𝑁! 8, 40 ,𝑃! 48, 24 , 𝑀 27, 33 ,𝑁 6, 30 & 𝑃(36, 18)
10.
11.
12.
𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟𝑠: 1. 52
2. 25
3. 34
4. 43
5. 73
6. 37
7. 29
8. 92
9. 43
10. 12
11. 31
12. 32
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DeterminingifPartsareSimilarForeachtriangle,lookforsimilarparts.Remember,similaranglesarethesame&similarsidefractionsareequal.13.
Areallgivensidessimilar?YESorNOAretheanglessimilar?YESorNO
14.
Areallgivensidessimilar?YESorNOAretheanglessimilar?YESorNO
15.
Areallgivensidessimilar?YESorNOAretheanglessimilar?YESorNO
16.
Areallgivensidessimilar?YESorNOAretheanglessimilar?YESorNO
17.
Areallgivensidessimilar?YESorNOAretheanglessimilar?YESorNO
18.
Areallgivensidessimilar?YESorNOAretheanglessimilar?YESorNO
Thereare 3SimilarTriangleProperties: SSS SAS AA 5CongruentTriangleProperties: SSS SAS ASA AAS HL and 1Propertyaboutwhathappensafteryouprovecongruence: CPCTC
Identifywhichpropertyisdescribedbyeachstatementbelow(mostpropertieswillappearmorethanonce).19.Iknowthat2sidefractionsandtheangleconnectingthemarethesameforbothtriangles,soIknowthatthetrianglesaresimilar.
20.Iknowthat2anglesandthesideconnectingthemarethesameforbothtriangles,soIknowthatthetrianglesarecongruent.
21.Iknowthatthetrianglesarecongruent,soIknowthatthe3sidesarethesameforbothtriangles.
22.Iknowthatthehypotenuseandoneoftheothersidesarethesameforbothrighttriangles,soIknowthatthetrianglesarecongruent.
23.Iknowthat2anglesarethesameforbothtriangles,soIknowthatthetrianglesaresimilar. 24.Iknowthat2sidesandtheangleconnectingthemarethesameforbothtriangles,soIknowthatthetrianglesarecongruent.
25.Iknowthatthetrianglesarecongruent,soIknowthat2anglesandthesideconnectingthemarethesameforbothtriangles.
26.Iknowthatthetrianglesarecongruent,soIknowthatthehypotenuseandoneoftheothersidesarethesameforbothrighttriangles.
27.Iknowthat3sidefractionsarethesameforbothtriangles,soIknowthatthetrianglesaresimilar.
28.Iknowthatthetrianglesarecongruent,soIknowthat2sidesandtheangleconnectingthemarethesameforbothtriangles.
29.Iknowthat2anglesandthesidethatisnotconnectingthemarethesameforbothtriangles,soIknowthatthetrianglesarecongruent.
30.Iknowthat3sidesarethesameforbothtriangles,soIknowthatthetrianglesarecongruent.
8 610 20 15
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45˚72˚45˚ 63˚
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