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| Concurrent line segments associated with a triangle |
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| Recall a line segment joining the vertex to the mid-point of the opposite side of a triangle. |
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| In DABC, AD is the line segment drawn from A to BC (opposite side of A). AD is a median of a triangle. |
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| "The line segment jointing a vertex of a triangle to the mid-point of the opposite is called a median of a triangle". |
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| A triangle has 3 vertices and 3 sides. Hence, three medians can be drawn in a triangle. |
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| Draw a triangle ABC. Mark the mid-points of BC, AC and AB as D, E and F respectively. Join AD, BE, CF. |
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| AD, BE and CF are the three medians of DABC. They pass through (or meet) at the same point (or common point). G is the point of concurrence of the medians. It is called as centroid. |
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| Centroid: The medians of a triangle are concurrent. The point of concurrence of the medians of a triangle is called centroid. Centroid is denoted by G. |
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| Recall a perpendicular drawn from a vertex of a triangle to the opposite side of a triangle. |
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| In DABC, AD is drawn perpendicular to BC. Draw a triangle PQR. Draw perpendiculars (altitudes) from P, Q and R to the opposite sides. The three altitudes meet at a point. Let this point be 'O'. O is the point of concurrence of the three altitudes of DPQR. |
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| The altitudes of a triangle are concurrent. The point of concurrency of the altitudes is called orthocentre. It is denoted by 'O'. |
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| In addition to the medians and altitudes as concurrent lines, we have the angle bisectors and perpendicular bisectors of the sides, which concur at a point. |
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