In a quadrilateral `A B C D` prove that `A B^2+B C^2+C D^2+D A^2=A C^2+B D^2+4P Q^2\ w h e r e\ P\ a n d\ Q` are middle points of diagonals `A C\ a n d\ B Ddot`

In a quadrilateral A B C D , prove that A B^2+B C^2+C D^2+D A^2=A C^2+B D^2+4P Q^2, where P and Q are middle points of diagonals A C and B Ddot

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In Figure, A D_|_B C and B D=1/3C Ddot Prove that 2C A^2=2A B^2+B C^2

In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^2=A C^2+B D^2 (ii) A B^2-B D^2=A C^2-C D^2

B D is one of the diagonals of a quadrilateral A B C Ddot\ \ A M\ a n d\ C N are the perpendiculars from A\ a n d\ C , respectively, on B Ddot Show That a r\ (q u a ddotA B C D)=1/2B Ddot(A M+C N)

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

In Figure, A D=A E\ a n d\ D\ a n d\ E are points on B C such that B D=E Cdot Prove that A B=A C

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E B G)=a r\ (\ E F C)

In Figure, A C=B C ,\ /_D C A=/_E C B\ a n d\ /_D B C=E A Cdot Prove that triangle D B C\ a n d\ E A C are congruent, and hence D C=E C\ a n d\ B D=A E