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.

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

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

ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD "||" BA as shown in the figure. Show that (i) angleDAC = angleBCA (ii) ABCD is a parallelogram

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

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.

In triangleABC , AD the perpendicular bisector of BC (see given figure). Show that triangleABC is an isosceles triangle in which AB=AC.

In /_\ABC , AB =AC =BC then it is ……….triangle .

In DeltaABC , AD is the perpendicular bisector of BC (See adjacent figure). Show that DeltaABC is an isosceles triangle in which AB = AC.

In a triangle ABC (see figure), E is the midpoint of median AD, show that (i) ar DeltaABE = ar DeltaACE (ii) ar DeltaABE=1/4ar(DeltaABC)