In Fig. 4.34, `A ,\ B` and `C` are points on `O P ,\ O Q` and `O R` respectively such that `A B P Q` and `B C Q R` . Show that `A C P R` . (FIGURE)

In Fig. 4.90, if P O S ~ R O Q , prove that P S Q R . (FIGURE)

In Fig. 4.90, if P S|| Q R , prove that P O S ~ R O Q . (FIGURE)

In Figure, S and T are points on the sides P Q and P R respectively of /_\ P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of /_\P S T and /_\P Q R .

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD . Show that a r\ (A P B)\ =\ a r\ (B Q C) .

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, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P || B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q) .

p\ A N D\ q are any two points lying on the sides D C\ a n d\ A D respectively of a parallelogram A B C Ddot\ Show that a r( A P B)=a r\ ( B Q C)dot

In fig.22, A B C is right angled at Adot\ Q\ \ a n d\ R are points on line B C and P is a point such that Q P||A C and R P||A B . Find /_Pdot

If a , b and c b respectively the pth , qth and rth terms of an A.P. prove that a(q-r) +b(r-p) +c (p-q) =0

In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q are extended to X\ a n d\ Y respectively and /_A B X=/_P Q Y . Prove that A B C~=\ P Q R .