Let's start at the first one. The first example would just be the easiest example possible, reacting a carbene directly with a double bond. This mechanism is going to look just like our other bridged ion mechanisms that made 3-ring intermediates. It's going to be a double bond grabbing the carbene and then the carbene grabbing back. This is going to show us that our product is cyclic. Now, whenever you add a ring to another ring, that ring has to be cis because if it was trans, you'd break the ring by having to straddle both sides of the original ring.
I'm just going to go ahead and draw this as a cis triangle or cis cyclopropane. I'm drawing it as going towards the top and then I would draw my methyl groups that were originally there going down. Now, this is not a chiral molecule, so that's my final answer. But if I had had some kind of asymmetry, then I would draw the enantiomer or just the stereo isomer that would be faced the other way.
Now, one thing to keep in mind about this, this is deceptively easy but there's one thing you need to keep in mind. These hydrogens could be swapped for any other atom that just likes to have one bond. For example, halogens, I could easily use a carbene that has let's say Cr2. If I did that, what would we need to add to this molecule? You would need to draw those bromines, guys. Here I'm just going to draw hydrogens since that's what I was using. But keep in mind that if it had been bromines or anything else, you would have to add them to the tip of the cyclopropane.
