`P` and `Q` are points on the sides `C A` and `C B` respectively of ` A B C`, right-angled at `C`. Prove that `A Q^2+B P^2=A B^2+P Q^2`.

P and Q are points on sides A B and A C respectively of A B C . If A P=3c m , P B=6c m , A Q=5c m and Q C=10 c m , show that B C=3\ P Q .

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.

In a A B C , P and Q are point on the sides A B and A C respectively, such that P Q B C . If A P=2. 4 c m , A Q=2c m , Q C=3c m and B C=6c m , find A B and P Q .

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 B C , P and Q are points on sides A B and A C respectively such that P Q B C . If A P=4c m ,\ \ P B=6c m and P Q=3c m , determine B C .

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 Qdot Prove that A Q=Q P

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P\ B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q)

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