In Figure, `O P ,\ O Q ,\ O R\ a n d\ O S` are four rays. Prove that `/_P O Q+\ /_Q O R+\ /_S O R+\ /_P O S=360^0`

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 Figure, P Q R S is a parallelogram, P O\ a n d\ Q O are, respectively, the angle bisectors of /_P\ a n d\ /_Q . Line L O M is drawn parallel to P Q . Prove that: P L=Q M (ii) L O=O M

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

In figure PS is the bisector of /_Q P R of DeltaP Q R . Prove that (Q S)/(S R)=(P Q)/(P R) .

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

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. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that /_R O S=1/2(/_Q O S-/_P O S)dot

A B C D IS A PARALLELOGRAM AND O is any point in its interior. Prove that: a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(^(gm)A B C D) Given: A parallelogram A B C D\ a n d\ O is a point in its interior. To Prove: a r\ (\ A O B)+\ a r( C O D)=a r\ ( B O C)+a r( A O D)

In Figure, A B C D is a ^(gm)dot\ \ O is any point on A CdotP Q\ A B\ a n d\ L M A Ddot Prove that a r(^(gm)D L O P)=\ a r\ (^(gm)B M O Q)