In Fig. 4.229, `A B D C` Prove that (FIGURE) ` D M U B M V` (ii) `D MxxB V=B MxxD U`

In Fig. 5.10, if A C=B D , then prove that A B=C D .

In Figure, it is given that A B=B C a n d A D=E Cdot Prove that a b e ~= C B D (ii) B D=B E

In Fig. 4.101, A D and C E are two altitudes of A B C . Prove that A E F ~ C D F (ii) A B D ~ C B E (iii) A E F ~ A D B (iv) F D C ~ B E C (FIGURE)

In Fig. 4.128, D E F G is a square and /_B A C=90o . Prove that A G F D B G (ii) A G F E F C (FIGURE) (iii) D B G E F C (iv) D E^2=B DxxE C

ABCD is a quadrilateral in which and /_D A B\ =/_C B A (see Fig. 7.17). Prove that (i) DeltaA B D~=DeltaB A C (ii) B D\ =\ A C (iii) /_A B D\ =/_B A C

In Fig. 4.179, A B C and D B C are on the same base B C . If A D and B C intersect at O , prove that (A r e a\ ( A B C))/(A r e a\ ( D B C))=(A O)/(D O) (FIGURE)

In fig., D is a point on hypotenuse AC of DeltaA B C ,D M_|_B C and D N_|_A B . Prove that (i) D M^2=D N*M C (ii) D N^2=D M*A N

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 Fig. 15.93, A B C D is a rectangle with A B=14\ c m and B C=7\ c m . Taking D C ,\ B C and A D as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region. (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)