SOLUTION
Consider the image in the below
From the diagram above,

Then we obtain the coordinate of H and G
Using the coordinate of midpoint formula,

Then

Then use the distance formula to fined the lenght of |EH| and |DG|
The Distance formula is given by
![\text{Distance}=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/56q6xjb5orq2dlg9dnnth7m4qxviq174d9.png)
Hence
![\begin{gathered} U\sin g\text{ the coordinatesH= (-h,k) and E= (2h,0) } \\ \text{Then} \\ |EH|=\sqrt[]{(2h-(-h)^2+(0-k)^2} \\ |EH|=\sqrt[]{(3h)^2+(-k)^2} \\ \text{Then } \\ |EH|=\sqrt[]{9h^2+k^2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/tt3bfuru86jwd40xpzy75ntckpk1tt6jgd.png)
Then
![\begin{gathered} \text Using the coordinatesG= (h,k) and D=(-2h,0) for \\ |DG|\text{ =}\sqrt[]{(-2h-h)^2+(0-k)^2} \\ |DG|=\sqrt[]{(-3h)^2^{}+(-k)^2} \\ \text{hence } \\ |DG|-=\sqrt[]{9h^2+k^2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/th1zswxbc3vp4cmim0nrjasp6cx3wrijei.png)
Hence
Since we obtain the same expression above
Then

therefore

Therefore
Answer: DG is congruent to side EH