and are respectively the bisectors of and such that and lie on sides and of and
respectively. If ,
Show that:
(i)
(ii)
(iii)
Similarity of triangle:
and are respectively the bisectors of and such that and lie on sides and of and respectively.
To Prove
If ,
(i)
(ii)
(iii)
Proof
(i) We have,
.
Therefore,
, and
Now, since,
(Angle bisector)
And,
In and ,
By similarity criterion, we have,
(ii) In and ,
Proved in part (i)
By similarity criterion,
(iii) In and ,
Since, we have already proved,
By similarity criterion,
Hence Proved