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Thread: the area of the triangles

  1. #1
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    Unhappy the area of the triangles

    Hello,
    I have a small problem, so I decide to ask You for a help.

    I don't know how improve that area AEF is equal to area of ABE and ADF triangels (together)

    Thank You for Your time
    Have a nice day
    Attached Thumbnails Attached Thumbnails the area of the triangles-zad4.png  
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  2. #2
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    Re: the area of the triangles

    Quote Originally Posted by rudzielica View Post
    Hello,
    I have a small problem, so I decide to ask You for a help.

    I don't know how improve that area AEF is equal to area of ABE and ADF triangels (together)

    Thank You for Your time
    Have a nice day
    you mean 'to prove' not 'improve'

    Let $H$ be the point symmetric of $D$ with respect to $AF$

    Area of triangle $AFH=$ area $AFD$

    similarly construct a triangle $AEK$ whose area is equal to the area of triangle $AEB$
    Last edited by Idea; Sep 21st 2019 at 11:58 AM.
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  3. #3
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    Re: the area of the triangles

    Thank You for a help and correction.

    However, I don't know where is point K?

    And there isn't informationa that DF+BE=FE
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  4. #4
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    Re: the area of the triangles

    $K$ is symmetric of $B$ w.r.t. the line $AE$

    $AFH$ and $AEK$ are right triangles

    angle $AHF=90$ degrees
    angle $AKE=90$ degrees

    Show that area $AFH+AEK=AFE$

    Note that $A,H,K$ are collinear
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