ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure) . Show that `Delta ABD cong Delta ACE`

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.

ABC is an isosceles triangle in which altitudes BD and CE are drawn to equal sides AC and AB respectively (see figure) Show that these altitudes are equal.

DeltaABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see figure). Show that /_BCD is a right angle.

Two sides AB, BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of DeltaPQR (See figure). Show that: (i) DeltaABM ~= DeltaPQN (ii) DeltaABC ~= DeltaPQR

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

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

Two sides AB, BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of trianglePQR (see figure). Show that: triangleABC~=trianglePQR

AD is an altitude of an isosceles triangle ABC in which AB = AC . Show that , AD bisects BC

The incircle of a triangle ABC touches the sides AB, BC and CA at the points F, D and E resepectively. Prove that AF + BD + CE + DC + EA = 1/2 (Perimeter of triangle ABC)