ABC is an isosceles trian gle in w h ich altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that ( i ) triangle ABE ~= triangle ACF (ii) AB = AC i.e ABC is an isoceles triangle

triangle ABC is an isosceles tr ia n g le in w h ich AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that angle BCD is a right angle.

ABC is an isosceles triangle in which AB=AC bisects exterior angle PAC and CD||AB (See the given figure ). Show that ABCD is a parallelogram

E and F are respec­tively the midpoints of equal sides AB and AC of triangle ABC (see the given figure). Show that BF = CE.

ABC is an isosceles triangle in which AB=AC bisects exterior angle PAC and CD||AB (See the given figure ). Show that /_DAC = /_BCA

AD and BC are equal perpendiculars to a line segment AB (see the given figure) Show that CD bisects AB.

D is a point on side BC of triangle ABC such that AD = AC (see the given figure). Show that AB gt AD.

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that angle ABD = angle ACD .

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

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