In figure D is a point on side BC of a `DeltaA B C`such that `(B D)/(C D)=(A B)/(A C)`. Prove that AD is the bisector of `/_B A C`.

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

D and E are points on sides AB and AC respectively of DeltaA B C such thata r" "(D B C)" "=" "a r" "(E B C) . Prove that D E" "||" "B C .

In Figure, A B C is a triangle in which /_B=2/_C . D is a point on side B C such that A D bisects /_B A C a n d A B=C DdotB E is the bisector of /_B . The measure of /_B A C is 72^0 (b) 73^0 (c) 74^0 (d) 96^0

In Figure, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles. Figure

A point D is taken on the side B C of a \ A B C such that B D=2D Cdot Prove that a r\ (\ A B D)=\ 2\ a r\ (\ A D C)

In fig., D is a point on hypotenuse AC of DeltaA B C ,D M_|_B C and D N_|_A B . Prove that (i) D M^2=D N*M C (ii) D N^2=D M*A N

In figure E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If A D_|_B C and E F_|_A C , prove that DeltaA B D ~DeltaE C F .

In figure, if DeltaA B E~=DeltaA C D , show that DeltaA D E~ DeltaA B C .

In Figure, A B C D is a trapezium in which A B||D C ,\ \ D C is produced to E such that C E=A B , prove that a r( A B D)=a r\ ( B C E)dot Construction: Draw D M\ on B A produced and B N_|_D C