Q) In the figure,AB=AC,D is the point in the interior of triangle ABC such that angle DBC=angle DCB. Prove that AD bisects angle BAC of triangle ABC.

Asked by banerjee_milky | 27th Jun, 2017, 07:51: PM

Expert Answer:

begin mathsize 16px style Given space that space AB equals AC space and space angle DBC equals angle DCB.
To space prove colon space AD space bisects space angle straight A
SInce space angle DBC equals angle DCB
So comma space DB equals DC space space.... left parenthesis sides space opposite space equal space angles space are space equal right parenthesis
space space space space space space space.... left parenthesis straight i right parenthesis
In space triangle ABD space and space triangle ACD comma
AB equals AC space space.... left parenthesis Given right parenthesis
AD equals AD space space.... left parenthesis Common space side right parenthesis
DB equals DC space space.... left parenthesis from space left parenthesis straight i right parenthesis right parenthesis
So comma space triangle ABD approximately equal to triangle ACD space space.... left parenthesis SSS space congruence space criterion right parenthesis
rightwards double arrow angle BAD equals angle CAD space space.... left parenthesis cpct right parenthesis
That space is comma space AD space bisects space angle BAC. end style

Answered by Rebecca | 28th Jun, 2017, 09:34: PM