Someone me i have to show how they're similar

Angle AXD = angle CXB (vertically opposite angle)
then angle ADB = angle ABC 
then angle DAB = angle BCD 
I couldn't remember the name of the rule 
I said that they are equal if you look at the curve AC and DB
They called them that two angles that subtended by the same mirror (arc)
lead them to be a similar angle (angle - angle - angle)

Where is the picture