Explain how you could use the construction tool or a compass and straightedge to create a line segment that is twice as long as
A and B
2 answers:
- Step 1) Plot point C that is not on segment AB
- Step 2) Draw a straight line through point C (convention usually has this line parallel to AB but it doesn't really matter)
- Step 3) Adjust the compass to be the width of AB. So one end of the compass is at point A, and the other end of the compass is at point B.
- Step 4) Keeping the same compass width, transfer the compass to the line through point C. Place the nonpencil part at point C. Then draw an arc that intersects the new line.
- Step 5) The intersection of the arc and line forms point D.
So far, segment CD is the same length as AB. So we can say AB = CD.
Let's keep going
- Step 6) Place the nonpencil part of the compass at point D and draw another arc to intersect line CD. Make sure you do not intersect at point C, but rather the point on the other side of D. Call this point E.
- Step 7) Use a marker or pen to highlight everything from C to E. So you'll highlight segment CE. Erase everything else.
Segment CE is composed of CD and DE, both of which are equal to AB. In other words, AB = CD = DE. Because CD = DE, and the two segments add up to CE, this must mean that CE is twice as long as CD. Therefore, CE is twice as long as AB.
See the diagram below for a visual summary.
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