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Math Help - Proving Similarity With Triangles

  1. #1
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    Proving Similarity With Triangles

    I still cannot prove this triangle being similar to the other one, if anyone can explain it that would be extremly grateful.

    Picture is linked

    Many thanks
    Attached Thumbnails Attached Thumbnails Proving Similarity With Triangles-capture.png  
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  2. #2
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    Re: Proving Similarity With Triangles

    Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. In other words, two triangles are similar if they have the same shape.

    In this case, the two triangles have different shapes. AED is clearly an equilateral triangle, while ABC is an scalene one, so they aren't similar.
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  3. #3
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    Re: Proving Similarity With Triangles

    Hello, JohnyyMal!

    The drawing is misleading. .(Mine is no better.)


    \text{Prove: }\:\Delta ABC \sim \Delta AED

    Code:
                A
                o
                 *
               *  *
                   *
              *     * C
                     o
             *     *  *
              θ  *     *
            *  *        *
             *           *
         B o              *
                           *
          *                 *
                          θ  *
       D o   *   *   *   *    o E

    \Delta ABC\text{ has: }\,\angle\theta\text{ and }\angle A.

    \Delta AED\text{ has: }\,\angle\theta\text{ and }\angle A.

    . . Hence, their third angles are equal.

    Therefore: . \Delta ABC \sim \Delta AED\;\;\;(a.a.a.)
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