In the first question, Since D is the midpoint of line segment AC. therefore, AD=DC.
In triangles, ABD & CBD. Since, AB is congruent to CB and BD is a common side between those two triangles. Therefore, AD is congruent to DC.
Finally, in triangles DEA & DEC Since, ED line segment is a common side between those triangles and the measure of angle EDA is as the same of angle EDC which are equal to 90 degrees and AD is congruent to DC. Therefore, triangle EDA is congruent to triangle EDC ( you have to take care of the triangle order letters in congruence) and EC is congruent to EA.
