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.

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 right angled at C. Prove that AB^2=2AC^2 .

Name the triangle in which two altitudes of the triangle are two of its sides.

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.

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

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 figure) Show that AD = AE

ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of /_\ABE and /_\ACD .

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

Can you think of a triangle in which the two altitudes of a triangle are two of its’sides?