If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.
Therefore the segments form the proportion:
BT is the midsegment of ΔMAH, therefore
DC is the midsegment of ΔBTH, therefore
Substitute:
cross multiply
divide both sides by HM
cross multiply
divide both sides by HM