Not necessarily. Although it is most likely you will get it around the same time as your mom, its not always guaranteed. My best friend got hers at 11 when her mom got it at 17! Everyone's body is different so there is a chance you may start earlier or later than your mom however its best to start preparing and talk to your mom about buying products just incase when you get close to the same age she got hers.

My mom got hers when she was 4 and my sister got hers before 5th grade (idk what age she was tho) and I'm 11 and haven't gotten mine, so I guess your period at a different age but I think it's more likely you get yours at a age similar to your moms.