In a given triangle ` A B C ,D E||B C` and `(A D)/(D B)=3/5dot` If `A C=5. 6` , find `A E` .

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=6\ c m , D B=9\ c m and A E=8\ c m , find A C . (ii) If (A D)/(D B)=3/4 and A C=15\ c m , find A E . (iii) If (A D)/(D B)=2/3 and A C=18\ c m , find A E .

If in two triangles A B C and D E F , (A B)/(D E)=(B C)/(F E)=(C A)/(F D) , then F D E C A B (b) F D E A B C (c) C B A F D E (d) B C A F D E

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 .

If A B C and DEF are two triangles such that A B C ~= F D E a n d A B=5c m , /_B=40^0 a n d /_A=80^0dot Then, which of the following is true? D F=5c m , /_F=60^0 (b) D E=5c m , /_E=60^0 D F=5 c m , /_E=60^0 (d) D E=5c m , /_D=40^0

If A B C and D E F are two triangles such that (A B)/(D E)=(B C)/(E F)=(C A)/(F D)=2/5 , then A r e a( A B C): A r e a( D E F)= 2:5 (b) 4: 25 (c) 4: 15 (d) 8: 125

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 an isosceles triangle ABC with A B" "=" "A C , D and E are points on BC such that B E" "=" "C D (see Fig. 7.29). Show that A D""= "A E

Fill in the blanks in the following so that each of the following statements is true Sides opposite to equal angles of a triangle are ....... Angle opposite to equal sides of a triangle are ....... In an opposite to equal sides of a triangle are ....... In a A B C if /_A=/_C , then A B= ..... If altitudes C E a n d B F of a triangle A B C are equal, then A B= ........ In an isosceles triangle A B C with A B=A C , if B D a n d C E are its altitudes, then B D is .......... C E In right triangles A B C a n d D E F , if hypotenuse A B=E F and side A C=D E , then A B C ~= ....

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

A B C is a triangle in which D is the mid-point of B C ,\ E\ a n d\ F are mid-points of D C\ a n d\ A E respectively. If area of A B C is 16\ c m^2, find the area of D E F