Altitudes the perpendiculars drawn from the vertices of a triangle to the opposite side are known as the altitudes of the triangle.

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

The sum of three altitudes of a triangle is

Prove that the perpendiculars drawn from the vertices of equal angles of an isosceles triangle to the opposite sides are equal.

If the altitudes from two vertices of a triangle to the opposite sides are equal,prove that the triangle is isosceles.

If the altitudes from two vertices of a triangle to the opposite sides are equal,prove that the triangle is isosceles.

Consider the following statements : 1. The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle. 2. The point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle may lie on two sides. Which of the above statements is/are correct ?

In a triangle ABC if angleA=theta and perpendiculars drawn from vertices B and C to respective opposite sides meet in P then find the value of angleBPC in terms of theta .