Draw a triangle ABC. Draw the perpendicular bisectors of its sides. The perpendicular bisectors of the sides of a triangle are concurrent (pass through the same point).
Recall the procedure to draw the perpendicular bisectors of the sides of a triangle.
- Draw DABC.
- With B and C as centres and radius equal to more than half of BC draw arcs of circles on either side of BC as to intersect at X and Y. Join XY (extend the bisecting line if needed).
- Similarly, draw the perpendicular bisectors of AB and AC.
- The three perpendicular bisectors of the sides of DABC pass through a common point (S).
Theorems on concurrence
Through the activities suggested you will find that the angle bisectors, the perpendicular bisectors of sides, the altitudes and the medians of a triangle are concurrent. Now medians of a triangle are concurrent. Now we shall prove these properties by logical deductions. The point of concurrency are stated as theorems and proved.
