Question

Points A and B are each at the centers of circles of radius AB.Compare the distance of EA to the distance EB.Compare the distance FA to the distance FB.Imagine drawing line EF.Write a conjecture about the relationshipOf line EF with AB.

Answer 1

ANSWER

Since EA = EB and FA = FB, then EF is a bisector of AB.

EXPLANATION

We have two circles such that AB is the radius of both circles.

If we look closely at the distance EA, we see that it goes from the centre A of the circle to point E on the circumference.

This means that EA is a radius.

The same applies for EB. It is a radius.

So, EA = EB

We also have that FA is a radius because it goes from the centres of the circle to a point on the circumference of the circle.

The same is true for FB.

So, FA = FB

As for EF, since EA = EB and FA = FB, then we have that EF must be a divide line AB into two equal parts.

Those are the lines EA, EB, FA, FB and EF.

A conjecture is a conclusion based on a piece of information earlier given. So, based on the information given:

Conjecture: Since EA = EB and FA = FB, then EF is a bisector of AB.