I have two right triangles that share a hypotenuse...

[tseday871221]

I have two right triangles: triangle BAD and triangle DCB. They share one hypotenuse, namely, DB. AB is parallel to DC and AD is parallel to BC. I have to write a congruency statement. Would you say that the triangles are congruent by SSS (side side side). If so, would it be because the parallel sides are congruent too?

 

[pka]

Angles \(\displaystyle \angle ADB\quad \& \quad \angle DBC\) are a pair alternate interiors in a parallel-transversal system. So are angles \(\displaystyle \angle DBA\quad \& \quad \angle BDC\). Do we then have ASA?

 

[soroban]

Hello, tseday871221!

I have two right triangles: \(\displaystyle \Delta BAD\) and \(\displaystyle \Delta DCB\).
They share one hypotenuse, namely, \(\displaystyle DB\).
\(\displaystyle AB\,\parallel\,DC\) and \(\displaystyle AD\,\parallel\,BC\).

I have to write a congruency statement.
Would you say that the triangles are congruent by SSS (side side side).
If so, would it be because the parallel sides are congruent too?

Did you notice that you have a rectangle?

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