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, A B C is a right triangle right angled at B and D is the foot of the the perpendicular drawn from B on A C . If D M_|_B C and D N_|_A B , prove that: (i) D M^2=D NxxM C (ii) D N^2=D MxxA N

A B C D is a rectangle. Points M and N are on B D such that A M_|_B D and C N_|_B D . Prove that B M^2+B N^2=D M^2+D N^2 .

In Figure, A D=B C\ a n d\ B D=C A . Prove that ∠A D B= ∠B C A a n d ∠D A B=∠ C B A .

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

In Figure, A B=A C\ a n d\ D B=D Cdot\ Prove that /_A B D=/_A C D

In right triangle A B C , right angle at C ,\ M is the mid-point of the hypotenuse A Bdot C is jointed to M and produced to a point D such that D M=C Mdot Point D is joined to point Bdot Show that A M C~= B M D (ii) /_D B C=/_A C B D B C~= A C B (iii) C M=1/2A B

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) M D_|_A C (iii) C M" "=" "M A=1/2A B

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) M D_|_A C (iii) C M= "M A=1/2A B

L\ a n d\ M are mid-point of two equal chords A B\ a n d\ C D of a circle with centre O . Prove that /_O L M=\ /_O M L (ii) /_A L M=\ /_C M L

In a \ A B C ,\ A D bisects /_A\ a n d\ /_C >/_Bdot Prove that /_A D B >\ /_A D C .