Предмет: Математика, автор: hilcenkonikita174


4. На стороні АС трикутника ABC вибрано точку М так, що ZABM = <C. Знайдіть довжину
відрізка МС, якщо АМ = 2 см, AB = 4 см​

Ответы

Автор ответа: liftec74
1

Ответ: MC=6 cm

Пошаговое объяснение:

Рассмотрим ΔАВС и ΔАМВ .

∡А  у них общий , а углы ∡ABM = <C ( по условию задачи).

Тогда  ΔАВС ~ ΔАМВ  ( по 2-м углам )

=> AB/AM= AC/AB

=> AB²=AC*AM => 4²=AC*2 =>AC=8  

AC=AM+MC => MC=AC-AM => MC=8-2=6 cm

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