`D ,\ E` and `F` are the points on sides `B C ,\ C A` and `A B` respectively of ` A B C` such that `A D` bisects `/_A ,\ \ B E` bisects `/_B` and `C F` bisects `/_C` . If `A B=5c m ,\ \ B C=8c m` and `C A=4c m` , determine `A F ,\ C E` and `B D` .

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

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

In a A B C ,\ D ,\ E ,\ F are the mi-points of sides B C ,\ C A\ a n d\ A B respectively. If a r( A B C)=16 c m^2, then a r\ (t r a p e z i u m\ F B C E)= 4\ c m^2 (b) 8\ c m^2 (c) 12 c m^2 (d) 10 c m^2

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x (ii) If A D=8 c m , A B=12 c m and A E=12 c m , find C E . (iii) If A D=4 c m , D B=4. 5 c m and A E=8 c m , find A C .

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

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 . (ii) A B=5. 6 c m , A D=1. 4 c m , A C=7. 2 c m a n d A E=1. 8 cm

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=10. 8 c m ,\ \ B D=4. 5\ c m ,\ \ A C=4. 8 c m\ a n d\ A E=2. 8 c m (ii) A D=5. 7 c m ,\ \ B D=9. 5 c m ,\ \ A E=3. 3 c m\ a n d\ E C=5. 5 c m .

In a A B C , A D is the bisector of /_B A C . If A B=8c m , B D=6c m and D C=3c m . Find A C 4c m (b) 6c m (c) 3c m (d) 8c m

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( A D F)=a r( D C E)dot

A B C D is a square E ,\ F ,\ G\ a n d\ H are points on A B ,\ B C ,\ C D\ a n d\ D A respectively, such that A E=B F=C G=D Hdot Prove that E F G H is square.