ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . Show that(i) `DeltaA P B~=\ DeltaC Q D`(ii) `A P\ =\ C Q`

In the given figure, ABCD is a parallelogram in which AN and CP are perpendiculars on diagonal BD. Prove that : (i) DeltaADN =DeltaCBP (ii) AN=CP

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 Q B~= DeltaC P D (iv) A Q = C P (v) APCQ is a parallelogram.

In Figure, A N and C P are perpendicular to the diagonal B D of a parallelogram A B C D . Prove that : (i) A D N~= C B P (ii) A N=C P

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC 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 N and C P are perpendicular to the diagonal B D of a parallelogram A B C Ddot Prove that : A D N~= C B P (ii) A N=C P

In Figure, two chords AB and CD intersect each other at the point P. Prove that: (i) DeltaA P C~ DeltaD P B (ii) A P*P B=C P*D P

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that : (i) S R || A C and S R=1/2A C (ii) P Q = S R (iii) PQRS is a parallelogram

In parallelogram ABCD two points P and Q are taken on diagonal BD such that DP = BQ (set figure). Show that: {:((i)DeltaAPD~=CQB,(ii)AP=CQ),((iii)DeltaAQB~=DeltaCPD,(iv)AQ=CP),((v)APCQ "is a parallelogram.",):} ltbegt

ABCD is a parallelogram where A (x, y), B (5, 8), C (4, 7) and D 2, -4). Find (ii) Equation of diagonal BD.

In figure, if DeltaA B E~=DeltaA C D , show that DeltaA D E~ DeltaA B C .