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⠀⠀⠀☞ A bissetriz é demonstrada pela soma dos ângulos internos de um quadrilátero e de um triângulo. ✅
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⠀⠀⠀➡️⠀Inicialmente temos um par de ângulos congruentes (α) na base e outro par de ângulos também congruentes no topo do trapézio (β). Observe que:
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[tex]\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(2,3){\line(1,0){4}}\put(0,0){\line(1,0){8}}\put(0,0){\line(2,3){2}}\put(8,0){\line(-2,3){2}}\put(1.5,3){A}\put(6.2,3){B}\put(-0.5,0){C}\put(8.2,0){D}\bezier(0.45,0.65)(0.8,0.6)(0.9,0)\put(0.4,0.2){$\alpha$}\bezier(7,0)(7.2,0.7)(7.55,0.65)\put(7.4,0.2){$\alpha$}\bezier(1.6,2.4)(2.6,2.4)(2.6,3)\put(1.8,2){$\ 180^{o} - \alpha$}\bezier(6.4,2.4)(5.2,2.4)(5.2,3)\put(4.5,2){$\ 180^{o} - \alpha$}\end{picture}[/tex]
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[tex]\Large\red{\boxed{\begin{array}{rcl}&\green{\underline{\footnotesize\text{$\sf Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly.$}}}&\\&\green{\footnotesize\text{$\sf \bullet~Experimente~compartilhar\rightarrow copiar~e~acessar$}}&\\&\green{\footnotesize\text{$\sf o~link~copiado~pelo~seu~navegador~ou~Browser.$}}&\\\end{array}}}[/tex]
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⠀⠀⠀➡️⠀Vamos agora traçar uma reta de C até B. Se observarmos o triângulo CAB notaremos que se trata de um triângulo isósceles, onde os dois ângulos desconhecidos podem ser chamados de x. Vejamos, pela propriedade da soma dos ângulos internos de um triângulo ser sempre 180º, o que podemos concluir:
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[tex]\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(2,3){\line(1,0){4}}\put(0,0){\line(1,0){8}}\put(0,0){\line(2,3){2}}\put(8,0){\line(-2,3){2}}\put(1.5,3){A}\put(6.2,3){B}\put(-0.5,0){C}\put(8.2,0){D}\bezier(0.45,0.65)(0.8,0.6)(0.9,0)\put(0.4,0.2){$\alpha$}\bezier(7,0)(7.2,0.7)(7.55,0.65)\put(7.4,0.2){$\alpha$}\bezier(1.6,2.4)(2.6,2.4)(2.6,3)\put(1.8,2){$\ 180^{o} - \alpha$}\bezier(6.4,2.4)(5.2,2.4)(5.2,3)\put(4.5,2){$\ 180^{o} - \alpha$}\bezier{60}(0,0)(3,1.5)(6,3)\put(0.7,0.6){$x$}\put(4.8,2.7){$x$}\end{picture}[/tex]
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[tex]\Large\red{\boxed{\begin{array}{rcl}&\green{\underline{\footnotesize\text{$\sf Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly.$}}}&\\&\green{\footnotesize\text{$\sf \bullet~Experimente~compartilhar\rightarrow copiar~e~acessar$}}&\\&\green{\footnotesize\text{$\sf o~link~copiado~pelo~seu~navegador~ou~Browser.$}}&\\\end{array}}}[/tex]
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⠀⠀⠀Como desejávamos demonstrar. ✌
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[tex]\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]☁
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⠀⠀⠀☃️ L͎̙͖͉̥̳͖̭̟͊̀̏͒͑̓͊͗̋̈́ͅeia mais sobre bissetrizes:
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https://brainly.com.br/tarefa/38398385 ✈
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[tex]\huge\blue{\text{\bf\quad Bons~estudos.}}[/tex] ☕
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[tex]\quad\qquad(\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios})[/tex] ☄
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[tex]\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }\LaTeX}[/tex]✍
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#SPJ4 [tex]\Huge\green{\text{$\underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~}$}}[/tex] ✞
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