In ` A B C` , `P` and `Q` are points on sides `A B` and `A C` respectively such that `P Q ||B C` . If `A P=3c m` , `P B=5c m` and `A C=8c m` , find `A Q` .

In A B C , P and Q are points on sides A B and A C respectively such that P Q||B C . If A P=4c m ,\ \ P B=6c m and P Q=3c m , determine B C .

In a A B C , P and Q are point on the sides A B and A C respectively, such that P Q// B C . If A P=2. 4 c m , A Q=2c m , Q C=3c m and B C=6c m , find A B and P Q .

P and Q are points on sides A B and A C respectively of A B C . If A P=3c m , P B=6c m , A Q=5c m and Q C=10 c m , show that B C=3\ P Q .

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

In /_\ P Q R , M and N are points on sides P Q and P R respectively such that P M=15 c m and N R=8c m . If P Q=25 c m and P R=20 c m state whether M N || Q R .

A B C D is a trapezium in which A B D C . P and Q are points on sides A D and B C such that P Q A B . If P D=18 , B Q=35 and Q C=15 , find A D .

In A B C , points P and Q are on C A and C B , respectively such that C A=16 c m , C P=10 c m , C B=30 c m and C Q=25 c m . Is P Q ||A B ?

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 a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

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.