In figure, `A D` and `B E` are respectively altitudes of an isosceles triangle `A B C` with `A C=B C` . Prove that `A E=B Ddot`

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD=AE. Prove that B,C,D,E are concylic.

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD=AE .Prove that B,C,D,E are concylic.

D a n d E are, respectively, the points on equal sides A B a n d A C of an isosceles triangle A B C such that B , C , E , a n d D are concyclic as shown in Figure. If O is the point of intersection of C D a n d B E , prove that A O is the bisector of line segment D E

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

In Fig. 4.124, 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, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles. 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, 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 .