The geometry of bromine trifluoride is a planar "T-shaped" molecule. The reason it is not trigonal planar is because of the lone two lone pairs of electrons on bromine. The fluorine atoms are repelled from the lone pairs causing it to have a unique shape. 

The same concept can be applied to Dihydrogen Monoxide (water). The geometry of water is "bent" because the lone pairs of electrons on the oxygen atom repel the hydrogen atoms, causing the bent shape.
Bromine Trifluoride molecule is in "Trigonal Planar" shaped with sp2 hybridized orbitals.Bond angle 120°.We can observe sp2-s sigma bonds between atoms of bromine and fluorine.