Question

additional practice problem set
unit 1 lesson 1 additional practice problems

1. here is a diagram of a straightedge and compass construction. explain why the length of segment xy is the same as the length of segment xz.

Explanation:

Step1: Recall circle - radius property

In a circle, all radii are equal.

Step2: Identify radii in the diagram

Points \(Y\) and \(Z\) lie on the circle with center \(X\). Segments \(XY\) and \(XZ\) are both radii of the circle centered at \(X\).

Answer:

Since \(XY\) and \(XZ\) are both radii of the same circle with center \(X\), by the property that all radii of a circle are equal in length, the length of segment \(XY\) is the same as the length of segment \(XZ\).