Ebikyusaganyo (Transformations)

From IALI NGO with authority from Muwanga Charles ! Ebikyusaganyo (Transformations) byetaagisa okunnyonnyoka emiramwa gino:

• Ekifaananyi (Picture)

• Ekifaananyo (Image

• Ekifaanaganyo (reflection)

• Obufaanagafu (similarity)

• Ekiseetuko (displacement)

• Ekyetoloozo (rotation)

• Eppeto (angle)

• Eppetero (bearing)

• Akaserengeto (slope)

• Ekiserengeto (gradient)

• Obuserengefu (steepness)

Sooka omanye enjawulo wakati w’ekiiseetulo n’ekiseetuko (displacement). Emiseetulo gya mirundi esatu:

i) Enkyetoloozo(rotation) . Wano waliwo okwetoolooza (turn)

ii) Ekifaanaganyo (reflection). Wano waliwo okuseetula mu bugalamivu (flip).Kino era kiyitibwa “kitunuuliganyo”

iii) Ekiseetuko (translation). Wano waliwo okuseetula mu busimba (vertical slide).

iv) Okuzimbulukusa n’okukkanya (okuzimbulukkanya).

(a) Bw’ozimbulukkanya (resize) enkula, oba ojigejjesa (ojizimbulukusa) oba okugikkakkanya(okujitoniya).

(b) Yadde enkula eno ojizimbulukkanyizza, zonna z’ozimbulukkanyizza zisigala zifaanagana (similar) , naye nga tezenkanankana (not congruent).

(c) Zonna ziba zigendana (are proportional). Okugendana si kye kimu n’okugendagana.

Obufaanagavu bw’enkula ez’ebitendero

           (Similarity of plane figures).

Singa okukyusa (okukendeeza oba okwongeza) ebigero byonna (all sizes) eby’enkula ez’ekitendero mu mugerageranyo gwe gumu (same ratio) , oguyitibwa omugerageranyo gw’obufaanagavu ( ratio of similarity ), kitegeeza nti enkula ezibaddewo n’eziddako ziba zifaanagana. Eky’okulabirako, ekikube (picture) n’ekifaananyi (photograph) kyakyo biba nkula ezifaanagana.

Mu nkula ebbiri zonna ezifaanagana amaweto agagendana (corresponding agles) gonna gaba genkanankana , ekitegeeza , singa  punkuti  A, B, C, D  ez’enkula emu  zigendana ne punkuti  a, b, c, d  ez’enkula endala , ekitegeeza   ABC =  abc ,  BCD =  bcd n’okweyongerayo. Mpuyinnyingi(polygons) ebbiri ( ABCDEF ne  abcdef  ) zifaanagana singa amaweto gazo gaba genkanankana  :  A =  a ,  B =  b , …,  F =  f , ate nga enjuyi zigendana/ za mugendaganyo (are proportional):

Omugendanyo gw’enpuyi gwokka ( proportionality of sides) tegumala kulaga nti mpuyinnyingi zifaanagana .

Engeri gy’otuuka ku bufaanagavu (similarity) bwa mpuyissatu.

Mpuyissatu ebbiri zifaanagana, singa:

(i) Amaweto gazo gonna agagendana gaba genkanankana

(ii) Enjuyi zazo zonna zigendana (za mugendaganyo)

(iii) Enjuyi bbiri eza mpuyissatu emu ziba zigendana n’enjuyi bbiri ez’endala era n’amaweto agali wakati w’enjuyi zino gaba genkana.

Mpuyissatu ennesembu ziba zifanagana singa:

(i) Amagulu gazo gaba gagendana

(ii) Okugulu n’omusittalo (hypotenuse) aga mpuyisstu emu gaba gagendana n’okugulu n’omusittalo ogw’endala.

(iii) Amaweto abiri aga mpuyissatu gaba genkanankana n’amaweto abiri ag’endala.

Obugaziyivu bw’enkula ezifaanagana bugendana ne kyebiriga za layini zazo ezifaanagana(nga enjuyi). N’olwekyo , obugaziyivu bw’ebikulungirivu bugendana n’ omugerageranyo(ratio) gwa kyebiriga za daamita oba ladiya.

Ekiseetuko

  (slide / translation)

Ekiseetuko eba nkula etambulizibwa ku lukoloboze (layini) nga bw’oseetula essowaani okuva ku muntu omu okudda mulala. kino kiseetuko kya mpuyisatu

Ekifaanaganyo (Ekitunuuliganyo)

Ekitunuuliganyo (flip) oba ekifaanaganyo ngeri ya kutambuza nkula okubuuka olukoloboze, okutondekawo ekifaananyo ky’endabirwamu eraga nga ebintu bitunuuliganye.

Ekyetoloozo (Rotation)

Ekiweto (turn) oba ekyetoloozo (rotation) kwe kuweta oba okwetolooza enkula.

Mu kibalangulo ebifaananganyo(transformations) n’olwekyo birimu ebika bino :

• Ekiseetuko oba ekiseetulo(Translation)

• Ekifaanaganyo(Reflection ). Manya enjawulo wakati w’ekifaananyo(image) , ekifaananyi(picture) , n’ekifaanaganyo(reflection).

• Ekyetoloozo oba ekyetoloolo(Rotation)

• Ekizimbulukkanyo( resizing).