Предмет: Математика, автор: ovechka071

найти углы равнобедренного треугольника, если известно, что прямая, проходящая через вершину угла при основании делит его на два треугольника, каждый из которых также является равнобедренным

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Автор ответа: sedinalana

ΔАВС,АВ=ВС
AD делит треугольник АВС на два равнобедренных ΔADB и ΔСAD
AD=BD⇒<DAB=<DBA=x⇒<ADB=180-2x⇒<ADC=2х как смежные
AC=AD⇒<ADC=<ACD=2х
<BAC=<BCA=2x
<BAC+<BCA+<ABC=180
2x+2x+x=180
5x=180
x=180:5
x=36-<ABC
36*2=72-<BAC и <BCA

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