Geometry Median Altitude

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What is Median in Geometry ?

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one running from each vertex to the opposite side. The median only bisects the vertex angle from which it is drawn in the case of equilateral triangles.

The three medians of a triangle are concurrent. The point of concurrency is known as the triangle's centroid, or centre of mass of the triangle which means that the centroid is always in the interior of the triangle. Two-thirds of the length of each median is between the vertex and the centroid, while one-third is between the centroid and the midpoint of the opposite side.The lengths of these two segments always have a constant ratio.

Properties of the median :

The medians of a triangle always intersect in one point (the centroid).
The centroid always lies inside the triangle.
The centroid divides the median into two segments. The lengths of these two segments always have a constant ratio of 2 : 1

What is an Altitude ?

In geometry, an altitude ...
... of a triangle is a straight line through a vertex and perpendicular to the opposite side or an extension of the opposite side. The intersection between the (extended) side and the altitude is called the foot of the altitude. This opposite side is called the base of the altitude. The length of the altitude is the distance between the base and the vertex.Since every triangle has three vertices it has three altitudes.The three altitudes of a triangle are concurrent. The point of concurrency is known as the triangle's Orthocenter.

Altitudes can be used to compute the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area, as well as being related to the sides of the triangle through trigonometric functions.

Altitudes of an acute triangle :

For an acute triangle all the altitudes are present in the triangle.

Altitudes for a right triangle :

For a right triangle two of the altitudes lie on the sides of the triangle, seg. AB is an altitude from A on to seg. BC and seg. CB is an altitude from C on to seg.AB. Both of them are on the sides of the triangle. The third altitude is seg. BD i.e.from B on to AC. The intersection point of seg. AB, seg. BC and seg. BD is B. Thus for a right triangle the three altitudes intersect at the vertex of the right angle.

Altitudes for an obtuse triangle :

D ABC is an obtuse triangle. Altitude from A meets line containing seg.BC at D. Therefore seg. AD is the altitude. Similarly seg.CE is altitude on to AB and BF is the altitude on to seg. AC. Of the three altitudes, only one is present inside the triangle. The other two are on the extensions of line containing the opposite side. These three altitudes meet at point P which is outside the triangle.

Properties of the altitude :

The altitudes of a triangle always intersect in one point.The point of intersection is called as Orthocenter.
If the triangle is acute, the intersection point lies inside the triangle. If the triangle is obtuse, the intersection point lies outside the triangle. If the triangle is a right triangle, the intersection point will coincide with the vertex which represents the right angle.

Comprehend more on about How to Find Perimeter of a Triangle and its Circumstances. Between, if you have problem on these topics Exterior Angle Theorem Please share your views here by commenting.