In a ` A B C ,\ \ B D` and `C E` are the altitudes. Prove that ` A D B` and ` A E C` are similar. Is ` C D B ~ B E C` ?

In A B C , A D and B E are altitudes. Prove that (a r( D E C))/(a r( A B C))=(D C^2)/(A C^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

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

In Figure, A C=A E ,\ A B=A D\ a n d\ /_B A D=/_E A Cdot Prove that B C=D E

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)

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, 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.

In Figure, it is given that A E=A D\ a n d\ B D=C Edot Prove that A E B\ ~= A D C

Fill in the blanks in the following so that each of the following statements is true. (i) Sides opposite to equal angles of a triangle are ....... (ii) Angle opposite to equal sides of a triangle are ....... (iii) In an equilateral triangle all angles are ....... (iv) In a A B C if /_A=/_C , then A B=\ ..... (v) If altitudes C E\ a n d\ B F of a triangle A B C are equal, then A B= ........ (vi) 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 . (vii) 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\ ~= ....