ABCD is a quadrilateral in which and`/_D A B"\ "=/_C B A` (see Fig. 7.17). Prove that (i) `DeltaA B D~=DeltaB A C` (ii) `B D"\ "="\ "A C` (iii) `/_A B D"\ "=/_B A C`

In quadrilateral ACBD, A C\ =\ A D and AB bisects /_A (see Fig. 7.16). Show that DeltaA B C~=DeltaA B D

In quadrilateral ACBD, A C\ =\ A D and AB bisects /_A (see Fig. 7.16). Show that DeltaA B C~=DeltaA B D

ABCD is a quadrilateral, then /_A+/_B+/_C+/_D=

If A B C D is a quadrilateral in which A B C D and A D=B C , prove that /_A = /_B .

If A B C D is a cyclic quadrilateral in which A D || B C . Prove that /_B=/_C

In Fig. 7.8, O A\ =\ O B a n d\ O D\ =\ O C . Show that (i) DeltaA O D~=DeltaB O C and (ii) A D\ ||\ B C

A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D intersect at P . If A B=D C , prove that: (i) P A B\ ~= P D C (ii) P A=P D\ a n d\ P C=P B (iii) A D || B C

D is a point on side BC of DeltaA B C such that A D\ =\ A C (see Fig. 7.47).Show that A B\ >\ A D .

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 .