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

ABC

C'

A'B' D

EF

F'

D'

E' GH

J J'

H'

G'

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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

25 30˚

30˚ 6

440˚40˚ 15

20

45˚72˚45˚ 63˚

8 12

16

6 915

7 24

2120˚20˚

8