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 figure E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If A D_|_B C and E F_|_A C , prove that DeltaA B D ~DeltaE C F .

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

In Figure, it is given that A B=E F ,B C=D E ,A B_|_B D and F E_|_C Edot Prove that A B D~=F E Cdot Figure

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

In figure, O is a point in the interior of a triangle ABC, O D_|_B C ,O E_|_A C and O F_|_A B . Show that (i) O A^2+O B^2+O C^2-O D^2-O E^2-O F^2=A F^2+B D^2+C E^2 (ii) A F^2+B D^2+C E^2=A W^2+C D^2+B F^2

If E is a point on side C A of an equilateral triangle A B C such that B E_|_C A , then A B^2+B C^2+C A^2= 2 B E^2 (b) 3 B E^2 (c) 4 B E^2 (d) 6 B E^2

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)

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, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prove that a r( A D E)=a r( B C F)

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