The perpendicular bisectors of sides of a triangle may be or may not be cevians. Do you agree with the statement? Justify your answer.

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Solution

Cevian: A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).

The perpendicular bisectors of an equilateral triangle are all cevians.

In an isosceles triangle, the perpendicular bisector of the non congruent side is a cevian and that of the congruent sides is not.

The perpendicular bisectors of the sides in a scalene triangle are not cevians.

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