In a ` A B C ,\ \ A D_|_B C` and `A D^2=B DxxC Ddot` Prove that ` A B C` is a right triangle.

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

In Figure, it is given that A B=C F , E F=B D a n d /_A F E= /_C B Ddot Prove that A F E= ~= C B D

The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot Prove that if B O=O D , the triangles A B C and A D C are equal in area. GIVEN : A quadrilateral A B C E in which its diagonals A C and B D intersect at O such that B O = O Ddot TO PROVE : a r( A B C)=a r( A D C)

The diagonals of quadrilateral A B C D , A C a n d B D intersect in Odot Prove that if B O=O D , the triangles A B C a n d A D C are equal in area.

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

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 ~= ....

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F Cdot Prove that A E\ C F is a parallelogram whose area is one third of the area of parallelogram A B\ C Ddot

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E