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 Figure, A B C is an isosceles triangle in which A B=A CdotC P A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

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

In Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q

ABC is an isosceles triangle in which AB=AC. If D and E are the mid-points of AB and AC respectively,prove that the points B,C,D and E are concyclic.

ABC is an isosceles triangle in which AB=AC. If D and E are the mid-points of AB and AC respectively,prove that the points B,C,D and E are concylic.

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 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

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

In Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A