Two Medians Of A Triangle Are Perpendicular. Any isosceles triangle with apex angle equal to 2arcsin1sqrt10 or 3686989765 degrees will have its medians to the equal sides perpendicular to each other. If a triangle is isosceles then the two medians drawn from vertices at the base to the sides are of equal length.
In the figure shown below the median from A meets the mid-point of the opposite side BC at point D. Medians A D. Opposite side is bisected by the median.
Medians A D.
If in a triangle two medians are perpendicular then the sum of the squares of the lengths of the sides to which these medians are drawn is 5 times greater than the squared length. Opposite side is bisected by the median. Two of the medians of a triangle are perpendicular to the opposite sides. An altitude of a triangle is the perpendicular drawn from any vertex to its opposite side whereas a median of a triangle is the line joining any vertex and the mid point of its opposite side.
