You are given two segments, with AB = 4 and with CD = 7. Explain how you could use only the congruent-segments construction to construct with EF = 1.
Not sure I understand your question but I'll give it a try.
AB = 4,
2 AB = 2 * 4 = 8
CD = 7
EF = 1
2AB - 1CD = EF
8 - 7 = 1
2x+63= 4x+2
To construct a segment EF with a length of 1 using only the congruent-segments construction, you can follow these steps:
1. Start by drawing segment AB with a length of 4 units.
2. Use the congruent-segments construction to construct a segment with a length of 7 units parallel to AB. This new segment will be labeled CD.
3. With point A as the center, construct a circle with a radius of 1 unit. Label the intersection points of this circle with the line containing segment CD as E and F.
Explanation:
The congruent-segments construction allows us to create a segment that is congruent to another given segment. In this case, we are given segment AB with a length of 4 units and segment CD with a length of 7 units. Our goal is to construct segment EF with a length of 1 unit.
To achieve this using only congruent-segments construction, we can utilize parallel lines and a circle with a radius of 1 unit. By drawing a parallel segment to AB, labeled CD, we can create a larger segment that is congruent to AB.
Then, by constructing a circle with a radius of 1 unit centered at point A, we can locate two points of intersection between this circle and the line containing segment CD. These intersection points, E and F, will be 1 unit away from point A, thus giving us segment EF with a length of 1 unit.