In Fig. 9.17, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) `a r"\ "(P Q R S)"\ "="\ "a r"\ "(A B R S)` (ii) `a r"\ "(A X"\ "S)"\ "=1/2"\ "a r"\ "(P Q R S)`

In Figure, P Q R S and A B R S are parallelograms and X is any point on side B Rdot Show that : a r(^(gm)P Q R S)=a r(^(gm)A B R S) a r(A X S)=1/2a r( P Q R S)

In Figure, P Q R S is a parallelogram. If X\ a n d\ Y are mid-points of P Q\ a n d\ S R respectively and diagonal S Q is jointed. The ratio a r\ (^(gm)\ X Q R Y):\ a r\ ( Q S R)= 1:4 (b) 2:1 (c) 1:2 (c) 1:2 (d) 1:1

P Q R S is a trapezium having P S\ a n d\ Q R as parallel sides. A is any point on P Q\ a n d\ B is a point on S R such that A B Q R . If area of P B Q is 17\ c m^2, find the area of \ A S R

In Figure, P Q R is a triangle and S is any point in its interior, show that S Q+S R

In Fig. 6.15, /_P Q R=/_P R Q , then prove that /_P Q S=/_P R T .

In a parallelogram PQRS (taken in order), P is the point (-1, -1), Q is (8, 0) and R is (7, 5). Then S is the point :

P Q R S is a parallelogram. P X\ a n d\ Q Y are respectively, the perpendiculars from P\ a n d\ Q to S R\ a n d\ R S produced. Prove that P X=Q Y

P Q R S is a rectangle inscribed in a quadrant of a circle of radius 13 c mdot A is any point on P Qdot If P S=5c m ,\ then find a r\ (\ R A S)

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.

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C 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.