Question

In triunghiul ABC ascutit unghic , inaltimea AM , cu M apatine [BC], este si mediana . Aratati ca triunghiul ABC este isoscel.

Answer 1

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Answer 2

$AM - mediana~\Rightarrow [BM] \equiv [MC] \\ \\ \Delta ABM~~|~~AM -comuna~~|~C.C \\ \Delta AMC~~|~~[BM] \equiv [MC]~~~| \Rightarrow \Delta ABM \equiv \Delta ACM \Rightarrow [AB] \equiv [AC] \\ \\ \\ \text{In} \Delta ABC \\ ~[AB] \equiv [AC] \Rightarrow \Delta ABC \text{ isoscel}$