You are given two segments, LineAB with AB = 4 and LineCD with CD = 7. Explain how you could only use the congruent-segments construction to construct LineEF with EF = 1.
AB = 4, CD = 7
2*AB = 8
1*CD = 7
2*AB - CD = 1
2*(4) - 7 = 1
8 - 7 = 1
To construct Line EF with EF = 1 using only congruent-segments construction, we can follow these steps:
Step 1: Draw horizontal Line AB with length AB = 4 units.
Step 2: Place the compass at point A and open it to a distance of 1 unit.
Step 3: Draw an arc above Line AB to intersect it at point E.
Step 4: Without changing the compass width, place the compass at point E and draw an arc intersecting Line AB below point B. Label this intersection as point F.
Step 5: Draw Line EF, connecting points E and F.
Step 6: Measure the length of Line EF using a ruler or compass, and it should be equal to 1 unit.
By using the congruent-segments construction, we have successfully constructed Line EF with EF = 1 unit.
To construct LineEF with EF=1 using only congruent-segments construction, you need to find a pair of segments whose lengths can be combined or manipulated to obtain the desired length, which is 1 in this case.
Step 1: Start by drawing LineAB with a length of 4 units.
Step 2: Use congruent-segments construction to find a segment that is equal in length to 7 units, which is the length of LineCD. Let's call this new segment LineGH.
Step 3: Now, combine LineAB and LineGH in such a way that their lengths add up to 1 unit. To achieve this, place LineGH at the endpoint of LineAB. Since LineAB has a length of 4 units and LineGH has a length of 7 units, when you place them together, you will have a segment LineEF, where EF = 1 unit.
By combining the segments LineAB and LineGH, we have created a new segment LineEF with a length of 1 unit, using only congruent-segments construction.