Altitude vs Perpendicular Bisector
Altitude and Perpendicular Bisector are two Geometrical terms that should be understood with some difference. They are not one and the same in definition. Altitude is a line from vertex perpendicular to the opposite side. The altitudes of the triangle will intersect at a common point. This common point is called as orthocenter.
It is interesting to note that there are separate formulas to solve the altitudes. If a, b and c sides of a triangle then you can solve on of the angles using the Cosine Law and you can also solve the altitude of the triangle by the formula of functions of a right triangle. This can be done if you know the area of the given triangle.
If the area of the given triangle is A, then the various altitudes of the triangle can be found out by using the formulas, namely, hA =2A/a, hB = 2A/b and hC = 2A/c
Perpendicular bisector has an altogether different definition. Perpendicular bisector of a triangle is a perpendicular that crosses through midpoint of the side of the triangle. This is the main difference between altitude and perpendicular bisector. It is interesting to note that vertex has to be taken into account in the case of finding the altitude whereas midpoint of the side is to be taken into consideration while finding the perpendicular bisector.
The three perpendicular bisectors are found out in a bid to find out the intersection point of the center of the circumscribing circle of the triangle. This is the purpose of knowing the perpendicular bisectors. This point of intersection is called as the circumcenter.
It is very important especially for the student of geometry to know the methods in determining the altitude and the perpendicular bisector. Different formulas are applied by the student to find them.