Understand Altitude, Median, Incentre and Circumcentre Of a Triangle. Altitude, Median, Incentre and Circumcentre Of a Triangle
Let us now learn about the Altitude, Median, Incentre and Circumcentre Of a Triangle.
Median of a triangle
In a triangle, a line joining the midpoint of a side to the opposite vertex is called the median.
Observed how you obtained the median from different types of triangles.
In each of the 3 triangles ABC. AD, BE and CF are the medians points de and f are the mid points of sides BC, CA and AB respectively. We need the point of intersection of the 3 medians as G.
Centroid of a triangle
In a triangle, the point where the three medians meet is called the Centroid of a triangle. In of each these triangles G is the centroid.
Altitude of a triangle
In a triangle, the perpendicular from a vertex to the opposite side is called the Altitude.
Observed how to construct the altitude from different types of triangles
In the first fig.: AD, BE, CF are the altitudes. O is the point of intersection of the 3 altitudes called the orthocentre. in the first fig. the orthocentre O lies inside the acute angled triangle.
In a right angled triangle the two perpendicular sides themselves form two of the altitudes. Hence, in fig. 2 : AB,BC and BD are the altitudes. The altitudes intersect at B. Hence, B is the Orthocentre.
Observe fig. 3 : The altitude from B is easily obtained as BE. The altitudes from A and C are obtained by producing sides BC and AB upto points D and F respectively. The Orthocentre is obtained by producing the altitudes AD, BD and CF until they intersect at O. Notice that O lies outside the obtused - angled - triangle.
Incentre of a triangle
In a triangle, the bisectors of the three angles meet at a point called the incentre. In triangle ABC, the bisector of the three angles meet at I. Hence, I is a incentre.
With I as a centre and taking IM as a radius of the compass. Draw a circle.
Notice that a circle touches the side of the triangle this is called Incircle.
Circumcentre Of a Triangle
In a triangle, the perpendicular bisectors of the three sides meet at a point called the Circumcentre.
In triangle ABC, OD, OE, OF are the perpendicular bisector of sides BC, AC and AB respectively. O is the Circumcentre.
With O as a centre and taking OA as a radius on the compass. Draw a circle
Notice that a circle passes through all the vertices, such a circle is called a Circumcircle.
Tags: Understand Altitude, Median, Incentre and Circumcentre Of a Triangle, mathematics_altitude_median_incentre_and_circumcentre_of_a_triangle, maths_altitude, maths_median, maths_incentre, maths_circumcentre, maths, Altitude, Incircle And Excircles Of A Triangle, Median (Literature Subject)