In ` A B C ,\ D` and `E` are the mid-points of `A B` and `A C` respectively. Find the ratio of the areas of ` A D E` and ` A B C` .

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a Delta A B C . Determine the ratio of the areas of D E F and A B C .

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

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 a A B C ,\ \ D\ a n d\ E are points on the sides A B and A C respectively. For each of the following cases show that D E// B C : A B=12\ c m ,\ \ A D=8\ c m ,\ \ A E=12\ c m\ a n d\ A C=18\ c m .

If D ,\ E and F are the mid-points of the sides of a /_\A B C , the ratio of the areas of the triangles D E F and ABC is .......

Let A B C D be a parallelogram of area 124\ c m^2 . If E\ a n d\ F are the mid-points of sides A B\ a n d\ C D respectively, then find the area of parallelogram A E F D

Let A B C D be a parallelogram of area 124c m^2dot If E and F are the mid-points of sides A B and C D respectively, then find the area of parallelogram A E F Ddot

A B C D is a trapezium with parallel sides A B=a\ a n d\ D C=bdot If E\ a n d\ F are mid-points of non-parallel sides A D\ a n d\ B C respectively, then the ratio of areas of quadrilaterals A B F E\ a n d\ E F C D is: a : b (b) (a+3b):(3a+b) (3a+b):(a+3b) (d) (3a+b):(3a+b)

In A B C ,\ D and E are points on sides A B and A C respectively such that A DxxE C=A ExxD B . Prove that D E B C .

In a A B C , D and E are points on A B and A C respectively such that D E||B C . If A D=2. 4 c m ,\ \ A E=3. 2 c m ,\ \ D E=2c m and B C=5c m , find B D and C E .