Triangle ABC has sides AC, BC and AB ...

[brucejin]

Triangle ABC has sides AC, BC and AB .If D is the midpoint of segment AB,is Area of triangle ADC the same as BDC?

Thanks

 

[mmm4444bot]

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[soroban]

Hello, brucejin!

Did you make a sketch?

In triangle ABC, D is the midpoint of segment AB.
is area of triangle ADC the same as BDC?

              C
              *
             *|* *
            * | *   *
           *  |  *     *
          *   |   *       *
         *    |h   *         *
        *     |     *           *
       *      |      *             *
    A * - - - * - - - * - - - - - - - * B
                      D

\(\displaystyle \text{Since }D\text{ bisects }AB,\;AD = DB.\)
. . The two triangles have the same base.

\(\displaystyle \text{The triangles have the same height, }h.\)

\(\displaystyle \text{What do you conclude?}\)