Question

(from unit 1, lesson 4.) 5. in the construction, a is the center of one circle, and b is the center of the other. explain why segment ea is the same length as segment bc. (from unit 1, lesson 2.)

Explanation:

Step1: Recall circle - radius property

All radii of a circle are equal.

Step2: Identify radii in circles

In the circle with center \(A\), \(EA\) is a radius. In the circle with center \(B\), \(BC\) is a radius.

Step3: Analyze the construction

The two circles are constructed in such a way that the distance between their centers \(A\) and \(B\) is used to define the radii of both circles. Since the construction implies that the radii of the two circles are equal (the circles are likely constructed with the same - length compass - setting), and \(EA\) is a radius of the circle centered at \(A\) and \(BC\) is a radius of the circle centered at \(B\), we can conclude that \(EA = BC\).

Answer:

Segment \(EA\) and segment \(BC\) are radii of circles with equal radii lengths, so \(EA\) is the same length as \(BC\).