Question

Given: D is the midpoint of segment AC, angle AED is congruent to angle CFD and angle EDA is congruent to angle FDCProve: triangle AED is congruent to triangle CFD

Answer 1

Since Angle AED is congruent to angle CFD and angle EDA is congruent to angle FDS, we can use the midpoint theorem to get the following:

`\begin{gathered} D\text{ is midpoint of AC} \\ \Rightarrow AD\cong AC \end{gathered}`

therefore, by the ASA postulate (angle,side,angle), we have that triangle AED is congruent to triangle CFD