In geometry, a vertex (plural vertices) is a point where two straight lines intersect. A triangle is formed by the intersection of three line segments. Each side of a triangle has two endpoints, with the endpoints of all three sides meeting at three different points in a plane, forming a triangle. The three different intersecting points or corners are called the vertices of a triangle.
How Many Vertices Does a Triangle Have
A triangle has three vertices or corners.
Vertices of a Triangle
△ABC is formed by three line segments
Side AB and AC intersect at point A, So, A is a vertex
Side AB and BC intersect at point B, So, B is a vertex
Side AC and BC intersect at point C, So, C is a vertex
Thus, in △ABC, ‘A’, ‘B’, and ‘C’ are the 3 vertices
Formula
How to Find the Vertices of a Triangle If the Midpoints of Its Sides are Given
If (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the midpoints of the 3 sides of a triangle, then we can find the vertices using the following formula:
How to Find the Vertices of a Triangle
Let us solve an example to understand the concept better.
Solved Example
(4, 1), (2, 5) and (3, 1) are the midpoints of the sides of a triangle. Find the vertices of the given triangle.
Solution:
Let A, B and C are three vertices of the given triangle. As we know, Vertex A = (x1 + x3 – x2, y1 + y3 – y2) Vertex B = (x1 + x2 – x3, y1 + y2 – y3) Vertex C = (x2 + x3 – x1, y2 + y3 – y1) Given, x1 = 4, y1 = 1 x2 = 2, y2 = 5 x3 = 3, y3 = 1 Putting the values we get, Vertex A = (x1 + x3 – x2, y1 + y3 – y2) = (4 + 3 – 2, 1 +1 – 5) = (5, -3) Vertex B = (x1 + x2 – x3, y1 + y2 – y3) = (4 + 2 – 3, 1 + 5 -1) = (3, 5) Vertex C = (x2 + x3 – x1, y2 + y3 – y1) = (2 + 3 – 4, 5 + 1 – 1) = (1, 5) Thus, the vertices of the given triangle are: A = (5, -3), B = (3, 5), and C = (1, 5)
