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Math Help - Area of Triangles in Trapezoid

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    Area of Triangles in Trapezoid

    How do you prove the area of Triangle A is congruent to Triangle B in this trapezoidArea of Triangles in Trapezoid-trap7.jpg?
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    Re: Area of Triangles in Trapezoid

    Quote Originally Posted by Aquameatwad View Post
    How do you prove the area of Triangle A is congruent to Triangle B in this trapezoidClick image for larger version. 

Name:	Trap7.jpg 
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    Do you have the lengths of the sides of the trapezium?
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    Re: Area of Triangles in Trapezoid

    No i don't have lengths. It is supposed to apply to any trapezoid. Now i found this link Trapezoid -- from Wolfram MathWorld which gives formulas as to why the areas are equal. But i don't understand why.
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    Re: Area of Triangles in Trapezoid

    Quote Originally Posted by Aquameatwad View Post
    No i don't have lengths. It is supposed to apply to any trapezoid. Now i found this link Trapezoid -- from Wolfram MathWorld which gives formulas as to why the areas are equal. But i don't understand why.
    Only having the area of the two triangles equal, does not imply that they are congruent.
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    Re: Area of Triangles in Trapezoid

    You are right badhi. So i guess the question is why do they have the same area?
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    Re: Area of Triangles in Trapezoid

    Hello, Aquameatwad!

    How do you prove the area of Triangle A is equal to Triangle B in this trapezoid?
    Code:
                P       Q
      -         *-------*
      :        *   *  *   *
      :       *  A  * *  B  *
      :      *    *      *    *
      h     *   *           *   *
      :    *  *       C        *  *
      :   * *                     * *
      :  **                          **
      - *-------------------------------*
        S                               R

    \Delta PSR\text{ and }\Delta QSR\text{ have the same base (SR) and the same height (h).}

    \text{Hence: }\:\text{area}(\Delta PSR) \;=\;\text{area}(\Delta QSR)
    . . . . . . . . . . A + C \;=\;B + C

    \text{Therefore: }\qquad\quad\; A \;=\;B

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    Re: Area of Triangles in Trapezoid

    Wow Soroban its that simple? I was trying to prove it by somehow by showing Triangle C was congruent to the Triangle with base PQ ( i guess we can call it D). which it is. Could i have used this information to prove A=B?
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