In a ` A B C ,\ \ A B=B C=C A=2a` and `A D_|_B C` . Prove that `A D=asqrt(3)` (ii) Area `( A B C)=sqrt(3)\ a^2`

In /_\ A B C , given that A B=A C and B D_|_A C . Prove that B C^2=2\ A C * C D

In /_\ A B C , if A D_|_B C and A D^2=B DxxD C , prove that /_B A C=90dot .

In a triangle A B C ,\ \ A D_|_B C and A D^2=B DxxC Ddot Prove that A B C is a right triangle.

In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A E_|_B C . Prove that: (i) A B^2=A D^2-B C* D E+1/4B C^2

In Figure, /_B A C=90dot and segment A D_|_B C . Prove that A D^2=B DxxD C .

In an equilateral A B C , A D_|_B C , prove that A D^2=3\ B D^2

In A B C , if B D_|_A C and B C^2=2\ A C C D , then prove that A B=A C .

Prove that the area of an equilateral triangle is equal to (sqrt(3))/4a^2, where a is the side of the triangle. GIVEN : An equilateral triangle A B C such that A B=B C=C A=a . TO PROVE : a r(triangle A B C)=(sqrt(3))/4a^2 . CONSTRUCTION : Draw A D_|_B C .

In a A B C ,\ \ B D and C E are the altitudes. Prove that A D B and A E C are similar. Is C D B ~ B E C ?

In figure /_A C B=90^@ and C D_|_A B . Prove that (B C^2)/(A C^2)=(B D)/(A D) .