Medians of Triangle
Question 1: Difference between Concurrent Lines and Intersecting Lines?
Answer:
Concurrent lines:
- At least three line segments pass through a single point.
- The point of intersection is known as the point of concurrency.
Intersecting lines:
- At least two line segments cross each other.
- The point of intersection is known as the point of intersection.
Question 2: What is a centroid?
Answer:
The centroid of any geometrical figure is the arithmetic mean position of all the points in the figure.
Question 3: Define orthocenter.
Answer:
The point at which all the altitudes of a triangle coincide is called the orthocenter of the triangle.
Question 4: Can the centroid and orthocenter be the same?
Answer:
Yes, for an equilateral triangle centroid and orthocenter are the same.
Related Resource
Prove that Medians of a Triangle are Concurrent
Concurrent lines are line segments, two or more, crossing through a single point of intersection. The point is called the point of concurrency. The point of concurrency is clearly visible in the case of triangles. These lines in the case of triangles are the altitudes, medians as well as perpendicular bisectors.
There are many lines of concurrency in the triangle which are discussed in this article.
Medians of Triangle
The line segment inside the triangle connects the vertex, to the side opposite to that vertex in the triangle. This line segment is known as the median. PS is the median in triangle QPR, where the bottom line segment, RS can be divided into two equal parts where QR = QS. The three medians of the triangle intersect at a point known as the centroid.
Altitudes of Triangle
The altitudes of a triangle emerge from each of the vertexes of the triangle and intersect each other at a single point known as the orthocenter.
Angle Bisectors
The line segments bisecting the angles from each of the vertices of the triangle are known as angle bisectors. There is a point of intersection for the angle bisectors, known as the incenter.
Perpendicular Bisectors
The line segments intersect the opposite sides of the triangle at right angles. These line segments go through a common point, which is known as the circumcenter.