Question

5 from unit 1, lesson 2 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.

Explanation:

Step1: Identify radii of circles

EA is a radius of the circle centered at A, so \( EA = AC \) (radii of the same circle are equal).
BC is a radius of the circle centered at B, and AC is also a radius of the circle centered at B (since C lies on the circle centered at B), so \( AC = BC \).

Step2: Transitive property of equality

By the transitive property, if \( EA = AC \) and \( AC = BC \), then \( EA = BC \).

Answer:

Segment \( EA \) and \( BC \) are equal because \( EA \) and \( AC \) are radii of the circle with center \( A \) (so \( EA = AC \)), and \( AC \) and \( BC \) are radii of the circle with center \( B \) (so \( AC = BC \)). By the transitive property of equality, \( EA = BC \).