What are constructions and what tools do we use?
How are they different from sketch or draw (measure)?
A compass with a set radius defines a distance. That distance is the radius of a circle. A partial "spin" of a compass creates an arc of a circle.
How did Euclid use the compass and straightedge as part of his deductive reasoning?
Why does the daisy have six petals and equilateral triangles?
We looked at our "daisy" construction and shared student results. We discovered that in our construction we had made: a regular hexagon, equilateral triangles, 60 degree angles, and 120 degree angles. These are now the foundation skills for our "tool belt", a set of construction skills that will allow us to synthesize and create more complicated constructions.
Students then worked their way through Euclid's Proposition 1 to figure out how to construct an equilateral triangle, and how to do it with just arcs instead of circles.
Then we created a set of notes to help us understand how to copy segments (add, or subtract, or double), and how to copy an angle (and double it). (Copy a segment and an angle are the next two skills in the tool belt.)
In this unit, it will be important to use the mathopenref website for the animations of constructions. There is a link below. There is also a link in the resources page under Pre-AP Geometry.
Tests were not seen yet. Make-ups were scheduled. A grade will be taken over HW #11 and #12 next time we meet.
HW #12: p 152-3: 1-8. Use plenty of paper. Leave arc marks so that we can see how you constructed. (Due Oct 2-3)
ALSO Due Thurs-Fri, Oct 4-5 - Construct and elaborate on a daisy design (p 10). More elaborate than just one plain 6-petal daisy. Add color. Use copy paper if possible. 5 pts