the side BC of triangle abc is produced such that D is on the ray BC the bisector of /_A meets BC IN L prove that angle abc+angle acd =2angle ALC

the side BC of triangle abc is produced such that D is on the ray BC the bisector of /_A meets BC IN L prove that angle abc+angle acd =2angle ALC

Q.37. If one angle of a triangle is 110$\xb0$, then the angle between the bisectors of exterior angles of the two angles is:

(A) 55$\xb0$

(B) 65$\xb0$

(C) 45$\xb0$

(D) 35$\xb0$

$19.ABCDisasquareandEFisparalleltoBD,Risthemid-pointofEF.Provethat\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(i\right)BE=DF\left(ii\right)ARbisects\angle BAD.$

Q.13. In figure, AD = BD. Prove that BD < AC.

9. ABC is a triangle in which $\angle $B=2$\angle $C. D is a point on BC such that AD bisects $\angle $BAC and AB=CD. Prove that $\angle $BAC=72

^{o}.

$\mathbf{20}\mathbf{.}In\u25b3ABC,EandDaretwopointslyingonABandACrespectivelysuchthatCEandBDintersecteachotheratO.If\u25b3AEC\cong \u25b3CDB,then\u25b3ABCwillalwaysbea/an$

(1) Obtuse-angled triangle

(2) Scalene triangle

(3) Isosceles right-angled triangle

(4) Equilateral triangle