Question

Can you think of a triangle in which two altitudes of the triangle are two of its side? Can altitude and median of a triangle be the same? What is special about the medians and altitudes of an equilateral triangle, an isosceles triangle and a scalene triangle?

Answer 1

I) According to Congruency Tests-- Theorem 1: If in a triangle, two altitudes are of equal length, then the triangle is isosceles. So, a triangle with 2 altitudes does exist, one of which is an ISOSCELES TRIANGLE. II) an isosceles triangle does have median=altitude. III) In an equilateral triangle, each altitude, median and angle bisector drawn from the same vertex, overlap. The isosceles triangle has two of its sides equal such that in a ∆ABC, AB = AC and BC is the base. Hence this median is also the altitude. In a Scalene triangle, none of them are equal.

Answer 2

Answer:

right angle triangle

so it has h1 = AC h2=AB these two are also the sides of the triangle