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Concurrent Lines - Three lines that intersect at a common point are called concurrent lines. Learn about the definition, concurrent lines of a triangle with some solved examples.
The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. Thm. 5-6: All of the # bis. of the sides of a k are concurrent.
Three or more lines that intersect at one point are said to be concurrent lines. The point that concurrent lines meet at is called the point of concurrency. A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side.
By definition, concurrent lines are lines that pass through a common point. In other words, concurrent lines have a single intercept point. All the triangle elements discussed in the previous paragraph are concurrent in the sense that all three altitudes, medians, angle bisectors, and perpendicular bisectors of a triangle are concurrent.
Three or more lines need to intersect at a point to qualify as concurrent lines. When three or more lines do intersect at a point, the point is called a point of concurrency. Incredibly, the three angle bisectors, medians, perpendicular bisectors and altitudes are concurrent in every triangle.
In a triangle, the concurrent lines are: The three altitudes of triangle from all the three vertices intersects each other at a common point. This point where the altitudes intersect is called the orthocenter. The three medians of triangle that divides the opposite side into equal parts and intersects at a single point, known as the centroid.
Several (that is, three or more) lines or curves are said to be concurrent at a point if they all contain that point. The point is said to be the point of concurrence. In analytical geometry, one can find the point of concurrency of any two lines by solving the system of equations of the lines.
