Opseg i površina pravokutnika

Ishodi:

[list][*]opisati pravokutnik[/*][*]imenovati vrhove, stranice i kutove pravokutnika[/*][*]imenovati nasuprotne stranice i vrhove pravokutnika[/*][*]nacrtati i opisati dijagonale pravokutnika[/*][*]nacrtati pravokutnik. [/*][/list][br][br]

Što je geometrijski lik?

[b][size=100][size=150]Geometrijski lik je dio ravnine omeđen dužinama ili zakrivljenim crtama, koje se ne sijeku.[br][/size][/size][/b][br][br]

Što je četverokut?

[b][size=150]Četverokut je dio ravnine omeđen četirima dužinama, uključujući i točke koje pripadaju tim dužinama.[/size][/b]

[size=200][b][color=#1e84cc]Upoznajmo pravokutnik.[/color][/b][/size]

Pravokutnik je geometrijski lik u ravnini. [br][img]data:image/png;base64,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[/img][br][color=#1e84cc][b][b]Pravokutnik je četverokut kojemu su svi kutovi pravi. [/b][br][br]Točke A, B, C i D su VRHOVI PRAVOKUTNIKA. [br][br]Duljine AB, BC, CD i AD su STRANICE PRAVOKUTNIKA. [br][br]Duljine stranica pravokutnika označujemo malim (pisanim) slovom.[/b][/color]

Nacrtan je pravokutnik. Ispravno mu označi vrhove i stranice. Izmjeri duljine njegovih stranica i označi ih uz pomoć priloženih alata. Izračunaj mu opseg, ako ti je poznato da je opseg zbroj duljina svih stranica.

[size=150][b][color=#1e84cc]Vrhovi pravokutnika koji pripadaju istoj stranici nazivaju se susjedni vrhovi,[br]a oni koji ne pripadaju istoj stranici nazivaju se nasuprotni vrhovi.[br][br]Vrhovi A i B su susjedni vrhovi, vrhovi A i C su nasuprotni vrhovi. [br][br]Nasuprotne stranice pravokutnika jednakih su duljina.[br][br]Nasuprotne stranice pravokutnika su paralelne.[br] [br]AB ∥ CD i AD ∥ BC[/color][/b][/size]

Nacrtan je pravokutnik ABCD. Izmjeri duljine njegovih stranica i označi ih uz pomoć priloženih alata. Izračunaj mu opseg, ako ti je poznato da je opseg zbroj duljina svih stranica

Što zaključuješ o nasuprotnim stranicama pravokutnika?

Što zaključuješ o susjednim stranicama pravokutnika?

Povucite kvadrate kako biste oblikovali pravokutnik. Obavezno upotrijebite sve kvadrate!

Možete li stvoriti pravokutnik koji se razlikuje od gore izrađenog? Pokušajte to učiniti!

Možete li stvoriti pravokutnik različit od dva koja ste napravili gore? Pokušajte to učiniti!

[size=150][b][color=#1e84cc]Stranice pravokutnika koje dijele zajednički vrh nazivaju se susjedne stranice. [br][br]Susjedne stranice pravokutnika međusobno su okomite.[br][br] |AB| ⊥ |BC|[br][br]Stranice koje nemaju zajednički vrh su nasuprotne stranice pravokutnika.[/color][/b][/size]