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

ABCD is a parallelogram in which /_A=70^(@) Compute /_B,/_C and /_D

ABCD is a parallelogram in which /_A=70^(@) Compute /_B,/_C and /_D.

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that D P = B Q . Show that: (i) DeltaA P D~= DeltaC Q B (ii) A P = C Q (iii) DeltaA B C (iv) A Q = C P (v) APCQ is a parallelogram.

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

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

DeltaA B C and DeltaD B C are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that (i) \ DeltaA B D~=DeltaA C D (ii) DeltaA B P~=DeltaACP (iii) AP bisects ∠ A as well as ∠ D (iv) AP is the perpendicular bisector of BC

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 Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that O B" "=" "O D . If A B" "=" "C D , then show that: (i) a r" "(D O C)" "=" "a r" "(A O B) (ii) a r" "(D C B)" "=" "a r" "(A C B) (iii) D A" "||" "C