` A B C` is a triangle right angled at `B ; a n d\ P` is the mid-point of `A C` . Prove that: `P Q\ _|_A B` (ii) `Q` is the mid point of `A B` (iii) `P B=P A=1/2A C`

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) M D_|_A C (iii) C M" "=" "M A=1/2A B

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B 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\ (\ P R Q)=1/2a r\ (\ A R C)

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)

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)

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

A B C is a triangle, P is a point on A Ba n dQ is a point on A C such that /_A Q P=/_A B Cdot Complete the relation (A r e aof A P Q)/(A r e aof A B C)=dot(())/(A C^2) .

A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D intersect at Pdot If A B=D C , prove that: P A B\ ~= P D C P A=P D\ a n d\ P C=P B (iii) A D B C

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.