If ` A B C\ ~= A C B ,` then ` A B C` is isosceles with
(a)`A B=A C` (b) `A B=B C` (c) `A C=B C` (d) `Non e\ of\ t h e s e`

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\ ~= ....

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

In Figure, A B C is an isosceles triangle with A B=A C\ a n d\ m\ /_A B C=50^0dot Find m\ /_B D C\ a n d\ /_B E C

In Figure, A B C is an isosceles triangle with A B=A C ,\ B D\ a n d\ C E are two medians of the triangle. Prove that B D=C E

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)

A B C is an isosceles triangle in which A B=A C,B E\ a n d\ C F are its two medians. Show that B E=C Fdot

B D and C E are bisectors of /_B and /_C of an isosceles A B C with A B=A Cdot Prove that B D=C Edot

In a A B C , D and E are points on A B and A C respectively such that D E||B C . If A D=2. 4 c m ,\ \ A E=3. 2 c m ,\ \ D E=2c m and B C=5c m , find B D and C E .

In Figure, if /_\ A B E~= /_\A C D , prove that /_\ A D E ~ /_\ A B C .

B D\ a n d\ C E are bisectors of /_B\ a n d\ /_C of an isosceles A B C with A B=A C . Prove that B D=C E