Given (Line segment) AB, explain how to construct a square with sides of length AB.
Can you help @Photon336
No!! It just that question, I think it about construction like with a compass and protractor. But i have no idea how to do that!
Oh. wait I see I would explain it by saying something like first you would take your compass and open it to the length of AB and then go through the steps right!
you could use the protractor to measure out the line segment
Protractors may not be used in classic Greek constructions - just a straighedge.
right a straight edge but would that be right if you did that then you would explain the steps=)
You cannot use any measuring device. Do you want me to show you a way to do the construction?
yes please, I'm confused =(
Start with a given segment AB. We do not know how many inches long it is. |dw:1444186643797:dw|
Next, draw a working line. On it, you will eventually mark off the length of segment AB.| dw:1444186761133:dw|
how do you draw a working line?
On the working line, locate a point (not an end point) and call it A. Draw a working line with the straightedge. No specific length. |dw:1444186886889:dw|
Go to the given segment AB. Open the compass. Place the sticky foot on point A. Stretch the compass so that the sticky foot stays on A while you open the compass just far enough to place the pencil end of the compass on point B. The sticky foot and the pencil foot are now the length of AB apart.
but isn't that a measuring tool? Because your telling how big the line is now?
Now, go to the working line and place the sticky foot on the point A on the working line. Swing the compass (draw an arc) with the sticky foot on A and when you swing the compass and intersect the working line, call that point B. Yes, we are measuring in a sense but not with a ruler. At no time will we have any lengths in inches.
ohh okay go on..
We will now make a right angle at A on the working line. Squares have right interior angles.
yep squares have 4 right angles lol!
do you accomplish this right angle with a protractor?
Close the compass to about 1/3 the width it had. Then, put the sticky foot on A and swing to the right and left of A. Do the same thing at point B using the SAME compass width. |dw:1444187336567:dw|
Open the compass a tiny bit more. Place the sticky foot on the point where the arc to the left of point A intersected the working line. From that point, swing an arc long enough to go above point A |dw:1444187611034:dw|
Now, put the sticky foot on the intersection of the arc to the right of point A and swing the same arc. Take note of where the two arcs intersect. |dw:1444187691528:dw|
>>do you accomplish this right angle with a protractor? NO, use a protractor at any point and the construction is incorrect. Put the protractor out of sight.
yeah I figured that out once u showed u next reply lol
The two arcs that were just drawn above point A - do the same for point B. |dw:1444187840266:dw|
Two points determine a line. Use the straightedge to join point A to the point determined by the intersection of the 2 arcs above point A. |dw:1444187914876:dw|
Do the same for B. |dw:1444187942531:dw|
oh i get it would you do the same for the top by using the compass in the same way to reach the top segment?
We have created right angles with vertices A and B. Now, get the measure of AB back on the compass.
With the measure of AB on the compass, place the sticky foot on A and draw an arc above A that intersects the extended segment we just drew upwards from point A. |dw:1444188127641:dw|
We clipped off length AB on that segment. Now, do the same for the extended segment from point B on the working line. |dw:1444188215585:dw|
ohh then you would do the same for b and then you would use u straigh edge right?
Yes. Last step coming up.
Use the straightedge to join the 2 points where the last arcs we drew intersected the lines extending upwards from points A and B on the working line. |dw:1444188336677:dw|
There is the constructed square with side AB. I named it square ABCD.
thank you so much!! i understand now lol
You are welcome.