CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.3 Question 10
10. CD and GH are respectively the bisectors of
and
such that D and H lie on sides AB and FE of
and
respectively. If,
~
, show that:
(i)
(ii)
~
(iii)
~
Solution (i)
It is given that
~
.
Therefore,
,
and
(1)
{Corresponding angles of similar triangles are equal}
{CD and GH are bisectors of
and
respectively} (2)
In
and
{From 1}
{From 2}
Therefore, from AA similarity criterion,
~
Therefore,
{Corresponding sides of similar triangles are in same ratio}
Solution (ii)
In
and
{Triangle ABC is similar to triangle FEG}
{Triangle ABC is similar to triangle FEG}
{CD and GH are bisectors of
and
respectively}
Therefore, by AA similarity criterion,
~
Solution (iii)
In solution (i), we have already proved that
~
which is same as
~
Hence Proved
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