Question

Can the altitudes and medians be same for a triangle?

Answer 1

The median and the altitude of an isosceles triangle can be the same.

To demonstrate the above mentioned statement,let's draw an isosceles triangle and draw a line that divides them into two equal parts.

The two sides of this triangle are equal because it is an isosceles triangle and the line drawn is perpendicular to the triangle and also it divides the base into two equal parts.

Let's analyse it below.
Draw a triangle PQR with PQ = PR and then draw a line segment PS perpendicular to QR.
PS is the altitude of the triangle.
It can be observed that the length of QS and SR is also the same by measurement.
Thus, S is the midpoint of QR. Therefore, PS is also a median of this triangle.

Hence, we can say that PS is the altitude and median of the isosceles triangle PQR.