Solution: If we see the figure we have that:

1. $\displaystyle \left[ AD \right]=\left[ DE \right]$

Because the point D is the middle point of the segment $ \displaystyle \left[ AE \right]$

2. $\displaystyle \left[ BD \right]=\left[ DC \right]$

Because the point D is the middle point of the segment

$\displaystyle \left[ BC \right]$

3. $\displaystyle \widehat{ADB}=\widehat{CDE}$ because they are opposite angles.

That’s why based on the the side – angle – side rule states that if two sides and the angle between those two sides are equal to the two sides and the angle between them of the other triangle, then those two triangles are congruent.

So, $\displaystyle \Delta $ABC and $\displaystyle \Delta $ CED are congruent.

In congruent triangles in front of congruent angles $\displaystyle \widehat{ADB}=\widehat{CDE}$

There are congruent side lengths $\displaystyle \left[ AB \right]=\left[ CE \right]$

From this we have that AB = CE, which means that AB = 10 cm.