Question

You are given two segments, AB with AB = 4 and CD with CD = 7. You want to construct a new segment, EF with EF = 1. If you can use only congruent-segments construction, explain how you would use AB and CD to construct EF.

Answer 1

Draw a line segment of sufficient length
Set your compass to length AB.
Mark off two segments of length AB on the new line. Call the endpoints E and G. EG has length 4+4=8.

Set the compass to the length of CD, or 7.

Place the compass at G and mark a point on EG between E and G. Call that F.

GF = 7, and EF = 1

Answer 2

12