Yes $\Delta ADB\ \cong\Delta CDB$

Yes $\Delta ADB\ \cong\Delta CBD$

No

Yes $\Delta BAD\cong\Delta BDC$

Yes $\Delta ACB\cong\Delta XYZ$

No

Yes $\Delta CBA\ \cong\Delta YXZ$

Yes $\Delta CBA\cong\Delta YZX$

Yes

NO

Yes

No

OEG

OGE

EGO

GOE

$\overline{DE}\ \cong\overline{AB}$

$\overline{ED}\cong\overline{AB}$

$\overline{BA}\cong\overline{ED}$

$\overline{CA}\cong\overline{CE}$

N is the midpoint of  $\overline{DP}$  

 $\angle D\cong\angle P$  

 $\overline{PG}\ \cong\overline{DG}$  

 $\overline{GN}\ \perp\ \overline{DP}$  

A

B

C

D

20

40

13

7

$\Delta XYZ\cong\Delta ZWX$

$\Delta WZX\cong\Delta YXZ$

$\Delta WXZ\cong\Delta YXZ$

$\Delta ZXY\cong\Delta XZW$