Question

1. this diagram was constructed with straightedge and compass tools. a is the center of one circle, and c is the center of the other. select all line segments that must have the same length as segment ab. a. ab b. ac c. bc d. bd

Explanation:

Step1: Recall compass - usage property

When using a compass, the distance between the two legs of the compass (radius) remains constant during a single - setting. If we set the compass to the length of segment AB (by placing one leg at A and the other at B), then any segment drawn with the same compass - setting will have the same length as AB.

Step2: Analyze each option

• Option A: Segment AB is the original segment itself, so it has the same length as AB.
• Option B: If we use the compass to transfer the length from AB to AC during the construction, and assuming proper use of the compass, AC can have the same length as AB.
• Option C: Similarly, BC can also have the same length as AB if constructed with the same compass - setting.
• Option D: There is no information or construction indication that BD has the same length as AB.

Answer:

A. AB, B. AC, C. BC