# Show that the perpendicular bisectors of the sides of a triangle are concurrent.

To prove:

Perpendicular bisectors of the sides of a triangle are concurrent.

Assuming:

ABC be a triangle with vertices A (x1, y1), B (x2, y2) and C (x3, y3).

Let D, E and F be the midpoints of the sides BC, CA and AB, respectively.

Explanation:

Thus, the coordinates of D, E and F are

Let mD, mE and mF be the slopes of AD, BE and CF respectively.

Slope of BC × mD = -1

mD

Similarly, the respective equations of BE and CF are

Let L1, L2 and L3 represent the lines (1), (2) and (3), respectively.

We observe:
1
L1 + 1L2 + 1L3 = 0

Hence proved, the perpendicular bisectors of the sides of a triangle are concurrent.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Straight line | Analyse your learning through quiz56 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 1169 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses