1. Benzer \u00dc\u00e7genler Kar\u015f\u0131l\u0131kl\u0131 a\u00e7\u0131lar\u0131 e\u015f ve kar\u015f\u0131l\u0131kl\u0131 kenarlar\u0131 orant\u0131l\u0131 olan \u00fc\u00e7genlere benzer \u00fc\u00e7genler denir.<\/p>\n
ABC ve DEF \u00fc\u00e7genleri i\u00e7in;
\noran\u0131 yaz\u0131l\u0131r. Buradan ABC \u00fc\u00e7geni ile DEF \u00fc\u00e7geni benzerdir denir ve
\nABC ~ DEF bi\u00e7iminde g\u00f6sterilir.
\n e\u015fitli\u011finde verilen k say\u0131s\u0131na, benzerlik oran\u0131 yada benzerlik <\/p>\n
katsay\u0131s\u0131 denir.
\nk = 1 olan benzer \u00fc\u00e7genlerde kar\u015f\u0131l\u0131kl\u0131 kenarlar e\u015fit oldu\u011fundan, bu \u00fc\u00e7genlere e\u015f \u00fc\u00e7genler denir.
\nABC ~ DEF benzerli\u011fi yaz\u0131l\u0131rken e\u015f a\u00e7\u0131lar\u0131n s\u0131ralanmas\u0131na dikkat edilir.<\/p>\n
2. A\u00e7\u0131 – A\u00e7\u0131 Benzerlik Teoremi
\nKar\u015f\u0131l\u0131kl\u0131 iki\u015fer a\u00e7\u0131lar\u0131 e\u015f olan \u00fc\u00e7genler benzerdir.<\/p>\n
3. Kenar – A\u00e7\u0131 – Kenar Benzerlik Teoremi
\n\u0130ki \u00fc\u00e7genin kar\u015f\u0131l\u0131kl\u0131 iki\u015fer kenar\u0131 orant\u0131l\u0131 ve bu kenarlar\u0131n olu\u015fturdu\u011fu kar\u015f\u0131l\u0131kl\u0131 a\u00e7\u0131lar e\u015f ise, \u00fc\u00e7genler benzerdir.<\/p>\n
ABC \u00fc\u00e7geni ile DEF \u00fc\u00e7geninin BAC ve EDF a\u00e7\u0131lar\u0131 e\u015f, bu a\u00e7\u0131lar\u0131n kenarlar\u0131 da orant\u0131l\u0131 ise, bu iki \u00fc\u00e7gen benzerdir.
\nBAC a\u00e7\u0131s\u0131n\u0131n k\u0131sa kenar\u0131n\u0131n EDF a\u00e7\u0131s\u0131n\u0131n k\u0131sa kenar\u0131na oran\u0131, BAC a\u00e7\u0131s\u0131n\u0131n uzun kenar\u0131n\u0131n EDF a\u00e7\u0131s\u0131n\u0131n uzun kenar\u0131na oran\u0131na e\u015fittir.<\/p>\n
4. Kenar – Kenar – Kenar Benzerlik Teoremi
\n\u0130ki \u00fc\u00e7genin kar\u015f\u0131l\u0131kl\u0131 b\u00fct\u00fcn kenarlar\u0131 orant\u0131l\u0131 ise bu iki \u00fc\u00e7gen benzerdir.<\/p>\n
Kenarlar\u0131 orant\u0131l\u0131 olan ABC ve DEF benzer \u00fc\u00e7genlerinde orant\u0131l\u0131 kenarlar\u0131 g\u00f6ren a\u00e7\u0131lar e\u015ftir.
\nm(A) = m(D),
\nm(B) = m(E),
\nm(C) = m(F)<\/p>\n
5. Temel Benzerlik Teoremi
\nABC \u00fc\u00e7geninde [DE] \/\/ [BC] ise y\u00f6nde\u015f a\u00e7\u0131lar e\u015f
\nolaca\u011f\u0131ndan ADE ~ ABC dir.<\/p>\n
A\u011f\u0131rl\u0131k merkezinden \u00e7izilen paralel do\u011fru kenarlar\u0131 1birime 2 birim oran\u0131nda b\u00f6ler. ABC \u00fc\u00e7geninde G a\u011f\u0131rl\u0131k merkezi ve [KL] \/\/ [BC]
\n|AK|=2|KB|
\n|AL|=2|LC|
\n6. Tales Teoremi
\nParalel do\u011frular kendilerini kesen do\u011frular\u0131 ayn\u0131 oranda
\nb\u00f6lerler. d1 \/\/ d2 \/\/ d3 do\u011frular\u0131 i\u00e7in
\nBuradan de elde edilir<\/p>\n
[AB] \/\/ [DE] ise olu\u015fan i\u00e7ters a\u00e7\u0131lar\u0131n e\u015fitli\u011finden, ABC ~ EDC olur. Buradan,
\ne\u015fitli\u011fi elde edilir. Buna kelebek benzerli\u011fi de denir.
\n7. Benzerlik \u00d6zellikleri
\nBenzer \u00fc\u00e7genlerin a\u00e7\u0131lar\u0131 kar\u015f\u0131l\u0131kl\u0131 olarak e\u015f, di\u011fer b\u00fct\u00fcn elemanlar\u0131 orant\u0131l\u0131d\u0131r.<\/p>\n
ABC ~ DEF \u00dbBurada k ya benzerlik oran\u0131 denir.
\na. Benzer \u00fc\u00e7genlerde orant\u0131l\u0131 kenarlara ait y\u00fcksekliklerin oran\u0131 benzerlik oran\u0131na e\u015fittir.<\/p>\n
b. Benzer \u00fc\u00e7genlerde orant\u0131l\u0131 kenarlara ait kenar-ortay uzunluklar\u0131n\u0131n oran\u0131 benzerlik oran\u0131na e\u015fittir.<\/p>\n
c. Benzer \u00fc\u00e7genlerde e\u015f a\u00e7\u0131lara ait a\u00e7\u0131ortay uzunluklar\u0131n\u0131n oran\u0131 benzerlik oran\u0131na e\u015fittir.<\/p>\n
d. Benzer \u00fc\u00e7genlerin \u00e7evrelerinin oran\u0131 benzerlik oran\u0131na e\u015fittir.<\/p>\n
e. ABC \u00fc\u00e7geninde i\u00e7te\u011fet \u00e7emberin yar\u0131\u00e7ap\u0131 rABC ve \u00e7evrel \u00e7emberin yar\u0131\u00e7ap\u0131 RABC , DEF \u00fc\u00e7geninde i\u00e7te\u011fet \u00e7emberin yar\u0131\u00e7ap\u0131 rDEF ve \u00e7evrel \u00e7emberin yar\u0131\u00e7ap\u0131 RDEF olsun.<\/p>\n
f. Alanlar oran\u0131
\nBenzer \u00fc\u00e7genlerin alanlar\u0131n\u0131n oran\u0131 benzerlik oran\u0131n\u0131n karesine e\u015fittir.<\/p>\n
g. Benzerlik oran\u0131 k = 1 olan \u00fc\u00e7genler e\u015f \u00fc\u00e7genlerdir.
\nKenarlar\u0131 e\u015fit aral\u0131kl\u0131 paralellerle b\u00f6l\u00fcnm\u00fc\u015f olan \u00fc\u00e7genlerde alanlar 1, 3, 5, 7 \u2026 gibi tek say\u0131larla orant\u0131l\u0131 olarak artar.<\/p>\n
[AB] \/\/ [EF] \/\/ [DC] benzerlik \u00f6zelliklerinden,<\/p>\n
|AB|.|FC|=|DC|.|BF|<\/p>\n
8. \u00d6zel Teoremler
\na. Menela\u00fcs
\nABC \u00fc\u00e7geni KM do\u011fru par\u00e7as\u0131 ile \u015fekildeki gibi kesiliyor ise
\nb. Seva
\nABC \u00fc\u00e7geni i\u00e7erisinde al\u0131nan bir P noktas\u0131 i\u00e7in, <\/p>\n","protected":false},"excerpt":{"rendered":"
1. Benzer \u00dc\u00e7genler Kar\u015f\u0131l\u0131kl\u0131 a\u00e7\u0131lar\u0131 e\u015f ve kar\u015f\u0131l\u0131kl\u0131 kenarlar\u0131 orant\u0131l\u0131 olan \u00fc\u00e7genlere benzer \u00fc\u00e7genler denir. ABC ve DEF \u00fc\u00e7genleri i\u00e7in; oran\u0131 yaz\u0131l\u0131r. Buradan ABC \u00fc\u00e7geni ile DEF \u00fc\u00e7geni benzerdir denir ve ABC ~ DEF bi\u00e7iminde g\u00f6sterilir. e\u015fitli\u011finde verilen k say\u0131s\u0131na, benzerlik oran\u0131 yada benzerlik katsay\u0131s\u0131 denir. k = 1 olan benzer \u00fc\u00e7genlerde kar\u015f\u0131l\u0131kl\u0131 kenarlar e\u015fit …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7281],"class_list":["post-3084","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-ucgenlerde-benzerlik"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3084","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3084"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3084\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}