Câu 4 ạ làm từ câu b trở đi ạ !!!!!!!!!

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Câu 4 ạ làm từ câu b trở đi ạ !!!!!!!!!
cau-4-a-lam-tu-cau-b-tro-di-a

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Phúc Điền 5 years 2021-05-23T04:50:30+00:00 1 Answers 17 views 0

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  1. kimchi2
    0
    2021-05-23T04:51:58+00:00
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    Giải thích các bước giải:

    a) Ta có:

    $\begin{array}{l}
    DE//AB\\
     \Rightarrow \left\{ \begin{array}{l}
    \widehat {EDC} = \widehat {ABC}\\
    \widehat {ADE} = \widehat {BAD} \Rightarrow \widehat {ADE} = \widehat {EAD} \Rightarrow \Delta AED \text{cân ở E} \Rightarrow EA = ED\left( 1 \right)
    \end{array} \right.
    \end{array}$

    Khi đó:

    $\begin{array}{l}
    \left\{ \begin{array}{l}
    \widehat Cchung\\
    \widehat {EDC} = \widehat {ABC}
    \end{array} \right.\\
     \Rightarrow \Delta EDC \sim \Delta ABC\left( {g.g} \right)\\
     \Rightarrow \dfrac{{ED}}{{AB}} = \dfrac{{EC}}{{AC}}\left( 2 \right)\\
    \text{Từ} \left( 1 \right),\left( 2 \right) \Rightarrow \dfrac{{EA}}{{AB}} = \dfrac{{EC}}{{AC}}\\
     \Rightarrow AC.EA = AB.EC

    \end{array}$

    b) Ta có:

    $\begin{array}{l}
    \left\{ \begin{array}{l}
    \widehat {API} = \widehat {DPE}\left( {dd} \right)\\
    \widehat {IAP} = \widehat {EDP}\left( {AI//DE} \right)
    \end{array} \right.\\
     \Rightarrow \Delta API \sim \Delta DPE\left( {g.g} \right)\\
     \Rightarrow \dfrac{{PI}}{{PE}} = \dfrac{{AI}}{{DE}}\left( 3 \right)
    \end{array}$

    Chứng minh tương tự có:

    $\begin{array}{l}
    \Delta BQI \sim \Delta EQD\left( {g.g} \right)\\
     \Rightarrow \dfrac{{QI}}{{QD}} = \dfrac{{BI}}{{ED}}\left( 4 \right)\\
    \text{Từ} \left( 3 \right),\left( 4 \right) \Rightarrow \dfrac{{PI}}{{PE}} = \dfrac{{QI}}{{QD}}\left( {do:AI = BI} \right)\\
    \text{Và} \Rightarrow \dfrac{{PI}}{{IE}} = \dfrac{{QI}}{{ID}}
    \end{array}$

    Khi đó:

    $\begin{array}{l}
    \left\{ \begin{array}{l}
    \widehat Ichung\\
    \dfrac{{IP}}{{IE}} = \dfrac{{IQ}}{{ID}}
    \end{array} \right.\\
     \Rightarrow \Delta IPQ \sim \Delta IED\left( {c.g.c} \right)
    \end{array}$

    cau-4-a-lam-tu-cau-b-tro-di-a

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