Question

please explain all the theorem of triangles ( class10)

Answer 1

given:in triangle ABC , DE ll BC
to prove :AD /DB =AE/EC
construction : join BE and EC ,EF perpendicular to AB, DG perpendicular AC
proof:EF perpendicular AB EF is the height of triangle ADE corresponding to AB
ar triangle =1/2×base×height
ar triangle ADE=1/2×AD×EF
similarly triangle DBE=1/2×DB×EF
ar triangle ADE=1/2×AD×EF/ar triangle DBE=1/2×DB×EF=AD/DB -(1)
DG perpendicular AC
DG is the height of triangle ADE corresponding to AC
ar triangle ADE =1/2 ×AE ×DG
similarly ar triangle ECD =1/2 ×EC ×DG
ar triangle ADE=1/2×AE ×DG /ar triangle ECD =1/2×EC ×DG =AE/EC -2
note that ar triangle DBE and triangle ECD are on the same base DE and between the same parallels line ar triangle DBE=ar triangle ECD-3
from 1,2,3 we get
AD/DB=AE/EC
hope this will help u