Transcript Slide 1

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.
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.
1) Draw a line
Use same radius
for both circles, so
segments are
congruent.
Modern, if I picked
up the compass
Writing
Center
of radius
and the
got
end
compass
moved, you’d
have
GREEN
to start allDRAWN
over,
DOT
would not PART
work
(compass
with a collapsable
and ruler)
compass.
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.
E
D
1) Draw a ray
2) Use original vertex, make radius.
F
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
triangles of different
1) draw
DrawSSS
a segment
lengths, although you will find that
2) Point at one end, pencil at the other, draw arc
the radii meet at different places.
3)
Switch
and
the
same left one.
Let’s
look at
the
bottom
4) Draw segments from intersection to endpoints.
Try the rest on your own, ask your
neighbors or your friends for help.
• HW #18: Pg 377: CE 2; Pg 378: 1, 3, 5-13,
15, 17, 18, 20, 22, 23, 25