The altitudes BN and CM of triangle ABC meet at H.Prove that triangle MHN is similar to triangle BHC.

Question

The altitudes BN and CM of triangle ABC meet at H.Prove that triangle MHN is similar to triangle BHC.

Answer 1

It will be pretty hard to follow this without a figure...but you should try.

∠BHM = ∠CHN 

∠BMH = ∠CNH = rt angle by construction

Therefore ΔBMH ∼ ΔCNH angles equal

Then in the triangles required you have two pairs of sides in proportion and the angle between them equal; therefore

the two triangles are similar.   QED