Given below is a parallelogram `A B C Ddot\ ` Complete each statement along with the definition or property used. (I) `A D=` (ii) `/_D C B=` (iii ) `O C=` (iv) `/_D A B+/_C D A=`

A B C D is a parallelogram in which /_A=70^0dot Compute /_B ,\ /_C\ a n d\ /_Ddot

In Figure, A B C D is a parallelogram, C E besects /_C\ a n d\ A F bisects /_Adot In each of the following, if the statement is true, give a reason for the same: /_A=/_C (ii) /_F A B=1/2/_A (iii) /_D C E=1/2/_C

In Figure, A B C D is a parallelogram in which /_D A O=40^0,\ /_B A O=35^0\ a n d\ /_C O D=65^0dot Find: (i) /_A B O\ (ii) /_O D C (iii) /_A C B (iv) /_C B D

If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O , and seqarate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D intersect at O and separate it into four parts such that a r( A O B)=a r( B O C)=a r( C O D)=a r( A O D) TO PROVE : Quadrilateral A B C D is a parallelogram.

If A B=7. 5 c m\ a n d\ C D=2. 5 c m , construct a segment whose length is equal to (i) A B-C D (ii) 2A B (iii) 3C D (iii) A B+C D (v) 2A B+3C D

In a parallelogram A B C D , the diagonals bisect each other at Odot If /_A B C=30^0,\ /_B D C=10^0a n d\ /_C A B=70^0, Find: /_D A B ,\ /_A D C ,\ /_B C D ,\ /_A O D ,\ /_D O C ,\ /_B O C ,\ /_A O B ,\ /_A C D ,\ /_C A B ,\ /_A D B

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X A Y B\ ~= C X D (iv) A X D~=\ C Y B

In Figure, A B C D is a trapezium in which A B ll C D and A D=B Cdot show that : /_A=/_B (ii) /_C=/_D (iii) A B C~= B A D (iv) Diagonal A C=diagnol B D

In Figure, A B C D is a parallelogram and E F C D is a rectangle. Also A L\ _|_D C . Prove that (i) a r(A B C D=a r(E F C D) (ii) a r\ ( A B C D)=D C x A L

In Figure, P is a point in the interior of a parallelogram A B C Ddot Show that a r( A P B)+a r( P C D)=1/2a r\ (|""|^(gm)A B C D) a r\ ( A P D)+a r\ ( P B C)=a r\ ( A P B)+a r( P C D)