10.1 Construction. Modern construction: Use a modern compass, you can maintain the radius as you pick up the compass and move it. Euclidean construction: Use a traditional compass, once it is picked up, the radius is lost. This is called a collapsable compass.
Modern construction: Use a modern compass, you can maintain the radius as you pick up the compass and move it.
Euclidean construction: Use a traditional compass, once it is picked up, the radius is lost. This is called a collapsable compass.
We will generally use modern construction as the book uses, but I will incorporate Euclidean construction where applicable. They will be denoted with the word Euclidean and modern
Copy a segment, modern.
Use same radius for both circles, so segments are congruent.
Modern, if I picked up the compass and the radius got moved, you’d have to start all over, would not work with a collapsable compass.
DRAWN PART (compass and ruler)
Center of compass
1) Draw a line
2) Choose point on line
3) Set compass to original radius, transfer it to new line, draw an arc, label the intersection.
Copy an angle.
Justification is SSS.
1) Draw a ray
2) Use original vertex, make radius.
3) Transfer radius to the ray you drew, and draw an arc.
4) Set radius from D and E, and transfer it to the new lines, setting the point on F and draw an intersection on the arc, then connect the dots.
Bisect an angle (Euclidean)
SSS (same radius, reflexive, same radius, CPCTC)
Why is it Euclidean? If I took the compass off, messed with it, I can still find my way back.
1) Draw an arc going across both sides of the angle.
2) Put point on one intersection, pencil on other, draw an arc so that it goes past at least the middle.
3) Flip it around and to the same.
4) Line from vertex to intersection.
Go to the back, let’s do the 600 angle first, and then work with the other parts.
The way to do this is to make an equilateral triangle.
SSS (same radius)
How would you manipulate this to make a 30 deg, 45 deg, 90 deg angle?
You use this same process to try to draw SSS triangles of different lengths, although you will find that the radii meet at different places. Let’s look at the bottom left one.
1) Draw a segment
2) Point at one end, pencil at the other, draw arc
3) Switch and the same
4) Draw segments from intersection to endpoints.
Try the rest on your own, ask your neighbors or your friends for help.