ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure) . Show that
`(i) DeltaABD ~= DeltaACE`
`(ii) AB = AC` i.e., ABC is an isosceles triangle.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show that vecBE+ vecDC=(3)/(2)vecBC .

In the figure, ABC is a triangle in which AB= AC. Points D and E are points on the side AB and AC respectively such that AD=AE. Show that points B, C, E and D lie on a same circle.

DeltaABC is an isosceles triangle in which AB = AC. Show that /_ B = /_ C.

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that, (i) AD bisects BC (ii) AD bisects /_ A.

In the figure, if BD bot AC and CE bot AB , prove that (i) Delta AEC~ Delta ADB " " (ii) (CA)/(AB)=(CE)/(DB)

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

ABC is a right angled triangle in which /_A = 90^@ and AB = AC . Show that /_B = /_C .

In the adjacent figure, ABC is a triangle in which angleB = 50^(@) and angleC = 70^(@) . Sides AB and AC are produced. If ‘z’ is the measure of the angle between the bisectors of the exterior angles so formed, then find 'z'.

In Fig. the incircle of △ABC, touches the sides BC, CA and AB at D, E respectively. Show that : AF + BD + CE = AE + BF + CD = ½ (Perimeter of △ABC).