In Fig. 4.241, `D E B C` and `A D=1/2B D` . If `B C=4. 5 c m` , find `D E` . (FIGURE)

In Fig. 4.95, if /_A D E=/_B show that A D E ~ A B C . If A D=3. 8 c m , A E=3. 6 c m , B E=2. 1 c m and B C=4. 2 c m , find D E . (FIGURE)

In Fig. 6.41, if A B|| D E , /_B A C=35^@ and /_C D E=53^@, find /_D C E .

In Fig. 6.41, if A B|| D E , /_B A C=35^@ and /_C D E=53^@, find /_D C E .

In Fig. 71, if A B C D\ a n d\ C D E F ,\ find \ /_A C E

In Fig. 4.140, /_A B C=90o and B D_|_A C . If A B=5. 7 c m , B D=3. 8\ c m and C D=5. 4 c m , find B C . (FIGURE)

In Fig. 4.125, F E C~= G B D and /_1=/_2 . Prove that A D E A B C . (FIGURE)

In Fig. 4.143, /_A=/_C E D , prove that C A B∼ C E D . Also, find the value of x . (FIGURE)

In Fig. 4.178, D E B C (FIGURE) If D E=4c m , B C=6c m and Area ( A D E)=16 c m^2 , find the area of A B C . (ii) If D E=4c m , B C=8c m and Area ( A D E)=25 c m^2 , find the area of A B C . (iii) If D E : B C=3:5 . Calculate the ratio of the areas of A D E and the trapezium B C E D .

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=2 c m , A B=6 c m and A C=9 c m , find A E . (ii) If (A D)/(B D)=4/5 and E C=2. 5 c m , find A E . (iii) If A D=x , D B=x-2 , A E=x+2 and E C=x-1 , find the value of x .

In Fig. 4.246, if P B C F and D P E F , then (A D)/(D E)= (FIGURE) 3/4 (b) 1/3 (c) 1/4 (d) 2/3