Starting with a clue from Brian Warner I came up with a list of interactive geometry programs. Several of them aspire to what I was seeking — something better than pencil and paper. The links with program name are to Wikipedia that generally tries more to way what the program does instead of selling it to you. The following dot links are to the main site.

GeoGebra iOS; Mac OS,
C.a.R. open source; Java
CaRMetal open source; Java
Graphmatica Free Trial Download
Kig Python
Euclidea Android

Try this! Compass and straightedge only. Has a set of problems to solve. HowTo