Question

In `DeltaABC`,ray BD bisects `angleABC` and ray CE bisects `angleACB`. If seg AB `cong`seg AC, then prove that ED `abs()` BC.

Answer 1

In `DeltaABC`
ray BD is the bisector of `/_ABC`
`:.` by the theorem of angle bisector of a triangle,
`(AB)/(BC)=(AD)/(DC)`……….. 1
In `DeltaABC`
ray CE is the bisector of `/_ACB`
`:.` by the theorem of angle bisector of a triangle,
`(AC)/(BC)=(AE)/(EB)`...............2
Set `AB~="seg"`.........Given 3
`:.(AB)/(BC)=(AC)/(BC)`............[From 1, 2 and 3 ]4
In `DeltaABC`
`(AE)/(EB)=(AD)/(DC)` ..[from 1, 2, 4]
`:.` by converset of basic propertionality theorem
set `ED||` side BC
i.e. `ED||BC`.