# Honors Geometry Companion Book, Volume 1

1.1.2 Measuring and Constructing Segments (continued)

Use a straightedge and a compass to construct a segment that is congruent to the given segment, PQ . Step 1 Using a straightedge, draw a segment that is longer than the given segment. Then, near one end of the drawn segment, draw and label a point. This is one of the constructed segment’s endpoints. Here, the drawn segment is longer than PQ and the endpoint is labeled A . Step 2 Place the compass so that its ends are at the given segment’s endpoints. Then, confirm that the compass is placed correctly by drawing a small arc that passes through the given segment’s endpoint. The compass is open to Q and P in this example. The drawn arc passes through P , so the compass is placed correctly. Step 3 Without moving the arms of the compass , place it on the drawn segment so that its tip is on the labeled point. Then use the compass to sketch an arc that intersects the drawn segment. Here, the tip of the compass is placed at A and the arc intersects the drawn segment at the opposite end. Step 4 Label the point where the arc intersects the drawn segment. This is the constructed segment’s second endpoint. In this example, the point where the arc intersects the drawn segment is labeled B . So, the constructed segment is AB . Since PQ and AB are congruent segments, they have the same length. So, AB = PQ .

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