In Figure, If `P Q=P T\ a n d\ /_T P S=/_Q P R ,` prove that `\ P R S` is isosceles

In Fig 7.51, P R\ >\ P Q and PS bisects /_Q P R . Prove that /_P S R\ >/_P S Q .

If P + Q = R and P - Q = S, prove that R^2 + S^2 = 2(P^2 + Q^2)

In Figure, P S D A is a parallelogram in which P Q=Q R=R S\ a n d\ A P B Q C Rdot Prove that a r\ (\ P Q E)=\ a r\ (\ C F D)dot

In Figure, A P _|_l a n d P R > P Q . Show that A R > A Q Given: A P_|_l a n d P R > P Q To Prove: A R > A Q Construction: Mark a point S on P R such that P S=P Qdot Join A S

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)

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

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

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

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

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