a) B M F D BMFD BMF D ⇒ F M B ^ = A D F ^ . \Rightarrow \widehat{FMB} = \widehat{ADF}. ⇒ FMB = A D F . △ A M B ∼ △ A D F ⇒ A B ⋅ A D = A M ⋅ A F ( 1 ) . \triangle AMB \sim \triangle ADF \Rightarrow AB \cdot AD = AM \cdot AF \quad (1). △ A MB ∼ △ A D F ⇒ A B ⋅ A D = A M ⋅ A F ( 1 ) . △ A E B ∼ △ A D H ⇒ A B ⋅ A D = A E ⋅ A H ( 2 ) . \triangle AEB \sim \triangle ADH \Rightarrow AB \cdot AD = AE \cdot AH \quad (2). △ A EB ∼ △ A DH ⇒ A B ⋅ A D = A E ⋅ A H ( 2 ) . ( 1 ) (1) ( 1 ) ( 2 ) ⇒ A M ⋅ A F = A E ⋅ A H ⇒ △ A E M ∼ △ A F H ⇒ A F H ^ = 90 ° . (2) \Rightarrow AM \cdot AF = AE \cdot AH \Rightarrow \triangle AEM \sim \triangle AFH \Rightarrow \boxed{\widehat{AFH}=90\degree}. ( 2 ) ⇒ A M ⋅ A F = A E ⋅ A H ⇒ △ A EM ∼ △ A F H ⇒ A F H = 90° .
b) A M AM A M H F ⊥ A M HF \perp AM H F ⊥ A M F F F A A A B , B, B , H , H, H , F , F, F , C C C
Fie A ′ A' A ′ A A A M . M. M . A B ∥ C A ′ ⇒ D C A ′ ^ = 90 ° AB \parallel CA' \Rightarrow \widehat{DCA'}=90 \degree A B ∥ C A ′ ⇒ D C A ′ = 90° H , H, H , F , F, F , C , C, C , A ′ A' A ′
Din (1) și (2) rezultă B , B, B , F , F, F , C , C, C , A ′ A' A ′ M M M ( B , F , C ) (B,F,C) ( B , F , C )
