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Fatima Contractor
Asked: 2022-11-07T11:13:09+05:30 In:

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

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

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