Question - 3 Kings losing hand

I have a question regarding a loss I just suffered in an online tournament.

*** TURN *** [Ks Kd 3c] [7h]
*** RIVER *** [Ks Kd 3c 7h] [Tc]

I had Kc/8d
My competitor had Kh/9d

I thought the 10c/7h on the board would play, but I guess since 8d and 9d are both higher, they played as the 5th card instead?

Thanks!

Yep, you have KKKT8 and you're opponent has KKKT9. You always play your 5 best cards so the T plays but the 7 doesn't.