# How do you construct perpendicular bisectors of a triangle?

Draw two circles of the the same radius equal to the length of given segment

To construct perpendicular bisectors of a triangle

The easy way to construct a perpendicular bisector

Here the centers of these circles are the endpoints of a given segment

What's more interesting is to prove that this construction delivers the perpendicular bisector.

Here is the proof.

Assume that

Hence:

So, we have proven that

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To construct perpendicular bisectors of a triangle, follow these steps:

- Draw the triangle using a ruler and pencil.
- For each side of the triangle, use a compass to draw arcs that are more than halfway across the side from each endpoint.
- Repeat step 2 for the other two sides of the triangle.
- Where the arcs intersect on each side, draw a point. These points are the midpoints of the sides.
- Use a straightedge to connect each midpoint to the opposite vertex of the triangle.
- The lines drawn in step 5 are the perpendicular bisectors of the triangle. They intersect at the circumcenter, which is equidistant from each vertex of the triangle.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has corners at #(3,7)#, #(4,1)#, and #(8,2)#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
- A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 1 , 4 )#, where is the other end?
- What is the orthocenter of a triangle with corners at #(5 ,4 )#, #(2 ,3 )#, and (7 ,8 )#?
- What is the centroid of a triangle with corners at #(3, 2 )#, #(5,5 )#, and #(12 , 9 )#?
- What is the orthocenter of a triangle with corners at #(4 ,9 )#, #(7 ,4 )#, and (8 ,1 )#?

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