Concurrency of perpendicular bisectors in triangle


Ask a Question, Get an Answer!
Hundreds of tutors are online and ready to help you right now!

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.

Note:

In proving theorems on concurrence, we draw two lines which intersect at a point and draw the third line in such a way that it passes through the point of intersection and then we prove that this straight line obeys the given conditions.


Ask a Question? Get an Answer!

connect to a tutor


Related Searches

perpendicular line of triangle abc

;,  

what will be the number of angles of three concurrent lines?

,  

straight line segment that passes

,  

perpendicular bisectors of a triangle

,  

bisectors

,  

sides of a triangle

,  

three sides live

,  

perpendicular

,  

drawing a triangle

,  

concurrency of altitudes in a triangle

,  

altitudes of triangle

,  

angle bisectors

...more