In Figure, `P Q R S` is a quadrilateral and `T\ a n d\ U` are respectively points on `P S` and `R S` such that `P Q=R Q ,\ /_P Q T=/_R Q U\ a n d\ /_T Q S=/_U Q Sdot` Prove that `Q T=Q Udot`

In Figure, P Q R S is a square and T\ a n d\ U are, respectively, the mid-points of P S\ a n d\ Q R . Find the area of O T S\ if P Q=8\ c mdot

In Figure, P Q R S is a quadrilateral. P Q is its longest side and R S is its shortest side. Prove that /_R > /_P a n d /_S > /_Q Given : P Q R S is a quadrilateral. P Q is its longest side and R S is its shortest side. To Prove : (i) /_R > /_P (ii) /_S > /_Q Construction : Joint P R a n d Q S

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

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

In Figure, /_Q P R=/_P Q R and M and N are respectively on sides Q R and P R of P Q R such that Q M=P N . Prove that O P=O Q , where O is the point of intersection of P M and Q Ndot

In Fig. 4.100, if (Q T)/(P R)=(Q R)/(Q S) and /_1=/_2 . Prove that P Q S ~ T Q R . (FIGURE)

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

P Q R S is a square such that P R\ a n d\ S Q intersect at Odot State the measure of /_P O Q

In Fig. 4.238, 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 . (FIGURE)

In Fig. 6.31, if P Q || S T , /_P Q R=110^@ \ a n d /_R S T=130^@ , find /_Q R S .