In ` a n d\ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q` are extended to `X\ a n d\ Y` respectively and `/_A B X=/_P Q Ydot` Prove that ` A B C~=\ P Q R`

In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q are extended to X\ a n d\ Y respectively and /_A B X=/_P Q Y . Prove that A B C~=\ P Q R .

In A B C and P Q R Figure, A B=P Q ,B C=Q R and C B and R Q are extended to X and Y respectively and /_A B X =/_P Q Ydot Prove that A B C~=P Q Rdot Figure

In A B C and P Q R Figure, A B=P Q ,B C=Q R and C B and R Q are extended to X and Y respectively and /_A B X = /_P Q Ydot Prove that A B C~=P Q Rdot Figure

In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ Q R\ a n d\ R P respectively. Prove that L N=M N .

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P to B C intersects F E\ at Q . Prove that A Q=Q P .

In Figure, bisectors of /_B\ a n d\ /_D of quadrilateral A B C D meet C D\ a n d\ A B produced at P\ a n d\ Q respectively. Prove that /_P+/_Q=1/2(/_A B C+/_A D C)dot

In Figure, P Q > P R. Q S\ a n d\ R S are the bisectors of /_ Q and /_R respectively. Prove that S Q > S R .

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ A R C)

p\ A N D\ q are any two points lying on the sides D C\ a n d\ A D respectively of a parallelogram A B C Ddot\ Show that a r( A P B)=a r\ ( B Q C)dot

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( R Q C)=3/8\ a r\ (\ A B C)