Center Controller reported vectoring aircraft off the SID causing controlled flight towards terrain.

Narrative

ATC combined; so a normal configuration. Aircraft X was cleared as filed up to 190 departing Runway XX at ZZZ. His route took him direct to his destination southeast bound. I was pretty busy with people looking for clearances and multiple arrivals. An aircraft missed their void time departing ZZZ1 and I had some arrivals trying to get in but we had to get that figured out first. So lots of stuff going on. The terrain rises very rapidly southeast of ZZZ. I noticed Aircraft X climbing out of 085 MSL or so and entering our 120 MIA. He was going to be in the 140 very shortly after and then the 160 around ZZZ2. I verified he had good visual on the terrain which he did; but I didn't want him to fly into the higher terrain if he didn't have to so I gave him a vector to the East to keep him in the 120 MIA while he was still at 090. The ZZZZ departure follows this route to the east out of ZZZ. I'm familiar with the geography of the area so between these two things I was comfortable taking the guy on a heading below the terrain. He was cleared as file off the ground so terrain obstruction is on him climbing out but I'd rather turn a guy below our MIA than let him fly into the side of a 14er.