Question

from unit 1, lesson 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 ba b ac c bc d bd e cd

Explanation:

Step1: Recall compass - construction property

In compass - and - straightedge construction, if we use the compass to measure the length of a line segment, all line segments drawn with the same compass - setting have the same length. If we set the compass to the length of segment AB, we are looking for segments that are radii of circles or equal - length segments constructed with the same compass opening.

Step2: Analyze the figure

Since the compass is used in construction, and assuming that the construction is based on equal - radius circles or equal - length segments set by the compass. Segment AC is a radius of a circle with center A (if the compass was set from A to B and then used to draw a circle centered at A, AC could be a radius of that circle). Also, if the construction is done correctly, segments that are constructed with the same compass opening as AB will have the same length. In a typical compass - and - straightedge construction, if we start with a length AB and use the compass to transfer that length, segments that are radii of circles drawn with the same compass setting as AB will be equal to AB.

Answer:

B. AC