We have seen how to bisect angles and how angle bisectors can be used to solve problems.

If it can be helpful to bisect the angles of a triangle, could it also be helpful if we know how to bisect the sides of the triangle?

• Explore perpendicular bisectors.
• Construct them using a compass and a straightedge.
• See how they can be used to solve problems.

When you call to order a pizza, how does the company decide which location to deliver your pizza from?

Consider the two pizzeria locations \(A\) and \(B\) on a map.

The pizza company can divide the city into two regions by drawing a perpendicular bisector through the line segment that joins \(A\) and \(B\).

All locations in the top-right region are closer to Pizzeria \(A\), while all locations in the bottom-left region are closer to Pizzeria \(B\).

If your home is at point \(H\), your order will be delivered from Pizzeria \(A\) because it is closer than Pizzeria \(B\).