Dividing a Segment Construction

by: Maggie Hendricks

To begin our construction we should construct a circle with center X and place a point C along its circumference.

Next construct a diameter of circle X through point C by constructing the ray. The point where the ray exits the circle should be called A.

Now construct another point along the circumference of circle X and call it Y. Using Y as a center andas a radius, construct a new circle Y.

 Construct the rayand label the point where it exits circle Y as B.

If we hide all that was used in our construction we see the desired image below.

The argument we will now investigate is that by construction,. See the proof below to show that this statement is valid.

since they are both radii of circle X

since they are both radii of circle Y

by the transitive property of equality


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