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

In Fig.4.97, if /_A=/_C, then prove that AOB~~COD.( FIGURE )

In Figure,/_E>/_A and /_C>/_D .Prove that AD>EC

In Fig. 4.124, E is a point on side C B produced of an isosceles triangle A B C with A B=A C . If A D_|_B C and E F_|_A C , prove that (i) A B D E C F (ii) A BxxE F=A DxxE 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

In Fig. 4.144, we have A B C D E F . If A B=6c m , C D=x\ c m , E F=10 c m , B D=4c m and D E=y\ c m , calculate the values of x and y . (FIGURE)

In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C B D

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. 10.78, if A D , A E and B C are tangents to the circle at D , E and F respectively. Then, (FIGURE) A D=A B+B C+C A (b) 2A D=A B+B C+C A (c) 3A D=A B+B C+C A (d) 4A D=A B+B C+C A

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=8x-7, D B=5x-3, A E=4x-3 and E C=(3x-1) , find the value of x . (ii) If A D=4x-3, A E=8x-7, B D=3x-1 and C E=5x-3 , find the volume x . (iii) If A D=2. 5 c m , B D=3. 0 c m and A E=3. 75 c m , find the length of A C .