Rockhound in Wyoming

I live in a rural area of Wyoming and I we have like 17 acres and pretty open hilly lots of rocks so we hike a lot and find really cool stuff. I found these two rocks today, one is a very nice agate. I cut the bottom off both. What I thought was petrified wood but now that I cut the bottom off I am not sure what it is so if anybody knows what it is let me know in the comments thank you.