`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`

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

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

Let A B C be an isosceles triangle in which A B=A C . If D ,\ E ,\ F be the mid-points of the sides B C ,\ C A\ a n d\ A B respectively, show that the segment A D\ a n d\ E F bisect each other at right angles.

In figure A B C is an isosceles triangle such that A B=A C\ a n d\ A D is the median to base B C . Then, /_B A D= 55^0 (b) 70^0 (c) 35^0 (d) 110^0

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\ ~= ....

In an isosceles triangle ABC with A B = A C , D and E are points on BCsuch that B E = C D (see Fig. 7.29). Show that A D= A 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

Let A B C be an isosceles triangle with A B=A C and let D ,\ E ,\ F be the mid points of B C ,\ C A\ a n d\ A B respectively. Show that A D_|_F E\ a n d\ A D is bisected by F E .

A B C is a triangle is which B E and C F are, respectively, the perpendiculars to the sides A C and A B . If B E=C F , prove that A B C is isosceles.

A B C is a triangle is which B E and C F are, respectively, the perpendiculars to the sides A C and A B . If B E=C F , prove that A B C is isosceles.