Question

How do you find the perpendicular bisectors of a triangle?

Answer 1

Hint: Here we will first form a triangle and choose a side which we want to bisect. Then we will use our compass to form two points above and below the chosen side of the triangle. Finally, we will connect the two points and show the perpendicular bisector of the triangle.

Complete step-by-step answer:
Let us consider a triangle $$\mathrm{\Delta }ABC$$ with sides $$AB,BC$$ and $$CA$$.

Now let us form a perpendicular bisector for side$$BC$$ using the following steps:
1. We will first take our compass with the length slightly bigger than the side $$BC$$.
2. We will put one pointer of the compass on one end-point of the line $$BC$$.
3. Then we will form an arc above and below the line $$BC$$.
4. Next, we will put the compass pointer on the other end-point of the line having the same length as the previous and again form an arc above and below the line cutting the previous arc and get two points as X and Y.
5. Now using the ruler we will draw a line joining the two points we have formed to get our perpendicular bisector.

In a similar way, we can bisect the other two sides also.

Note:
A perpendicular bisector of a side of the triangle is the line coming from the vertex opposite to that side which divides the sides into two equal parts. A median is a line that comes from the vertex of a triangle towards the side opposite of that vertex at its midpoint. In equilateral triangles, the median is always the perpendicular bisectors. A perpendicular bisector forms a right angle with the line it bisects.