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Thread: [SOLVED] Please help! 2 Trapezoid problem

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    [SOLVED] Please help! 2 Trapezoid problem

    see attachement.
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) $\displaystyle AB=AD, \ AE=DF, \ \widehat{BAF}=\widehat{ADF}\Rightarrow $

    $\displaystyle \Rightarrow\Delta ABE\equiv\Delta DAF\Rightarrow\widehat{AEB}=\widehat{AFD}, \ \widehat{ABE}=\widehat{DAF}$

    $\displaystyle \widehat{BPF}=\widehat{APE}=180^{\circ}-(\widehat{EAP}+\widehat{AEP})=180^{\circ}-(\widehat{DAF}+\widehat{AFD})=$

    $\displaystyle =\widehat{D}=180^{\circ}-\widehat{C}=120^{\circ}$

    2) $\displaystyle \widehat{ADB}=\widehat{ABD}=\widehat{BAC}=\widehat {BCA}=\alpha$

    In $\displaystyle \Delta ABD$ we have $\displaystyle 3\alpha+90^{\circ}=180^{\circ}\Rightarrow\alpha=30 ^{\circ}$

    $\displaystyle \Rightarrow\widehat{DAB}=120^{\circ}\Rightarrow\wi dehat{BCD}=60^{\circ}$
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