What is the difference between altitude and median in geometry

Usually, medians, angle bisectors and altitudes drawn from the same vertex of a triangle are different line segments. But, importantly, in special triangles such as isosceles and equilateral triangles, they can overlap. And, as always, any time you can identify a triangle as a special triangle, you have even more rules you can apply to better understand it.

We will now give you some of these properties which can be very useful. In an isosceles triangle where base is the side which is not equal to any other side :. Hence this angle bisector is also the altitude. Hence this altitude is also the angle bisector. Hence this median is also the altitude. In an equilateral triangle , each altitude, median and angle bisector drawn from the same vertex, overlap.

Angle bisector which is also a median implies isosceles triangle which implies it is also the altitude. A median which is an altitude implies the triangle is isosceles which implies it is also the angle bisector.

The angle bisector is also a median. But we have no idea about the measure of angle A. This statement alone is not sufficient. The altitude is also a median. So the triangle is equilateral! So angle A must be 60 degrees. Therefore the correct answer is C. And the ever-important takeaway from this problem: here we were able to use our knowledge of how medians, altitudes, and angle bisectors appear in special types of triangles to prove that we were dealing with a special, equilateral triangle.

It is drawn from a vertex of the triangle to the opposite side being perpendicular to it. Divides the opposite side into two equal parts or halves. It may or may not divide the opposite side into two equal parts or halves. Explore math program. The median bisects the angle of the vertex.

It also divides the area of the triangle in half. Likewise the altitudes, there is a unique median for each side; therefore every triangle has three medians. All the three medians together divide the triangle into six smaller triangles with the same area.

Refer diagram. The three medians of the triangle intersect at a point, which divides each median to ratio. It is known as the centroid of the triangle and, for a uniform laminar triangle the center of mass is located here.

Both the orthocenter and the median lie on the Euler line, which also contains the circumcenter of the triangle.