Triangle Midsegment Theorem Examples

DG is a midsegment of ∆ABC. If AB =12, how long is DG?

Well, midsegments are half the length of the side they're parallel to. Since its parallel side AB has a length of 12, we know that DG will be 6 units long.

EF is a midsegment of ∆ABC. If AE = 3, how long is EB? If EF = 15, how long is BC?

Since EF bisects AB, we know that AE ≅ EB. So EB is 3.

And since the midsegment EF has a length of 15, BC has a length twice that, or 30.

HF = 14 and BC = 28. Is HF a midsegment of ∆DGC?

Hmmm. If HF were a midsegment of ∆DGC, then GC must be 28. But we know that BC is 28.

Since BG is obviously greater than 0, then GC is less than 28. So in this case, no, HF is not a midsegment.