This project requires you to demonstrate an understanding of 5 geometry theorems/postulates/shapes by creating festive ornaments. Don't leave me to imagine a theorem on your ornament. It should be marked so that anyone who did not know math could make sense of it.
It will be worth two grades. A test grade based on content and a quiz grade based upon presentation. Presentation may include your name, the theorem, appropriate markings, creativity and originality. Use a festive theme such as Christmas, Hanukah, Winter Solstice, Kwanzaa, etc. Ethnic and cultural heritage can be a great source of creative ideas for a project like this.
To earn an A: Choose 5 items from the theorem list and correctly demonstrate them with your ornament(s).
To earn a B: Choose a combination of 5 items from either the list of theorems or shapes and correctly demonstrate them with your ornament.
To earn a C: Choose 6 items from the list of shapes and correctly demonstrate them with your ornament.
Frequently the best materials are in a junk drawer or "Aunt Lucy's" no longer used craft supplies.
Project Guidelines:
1. Students may work alone or in pairs,
2. choosing five items from the list,
3. to create an ornament(s) that must be 4 to 9 inches in height.
4. Each ornament must be clearly labeled & with string.
5. Be creative, colorful, festive and culturally resourceful!
The emphasis is on quality not quantity. So no more than one theorem per ornament.
If you have questions about what might/might not be acceptable, see me in class!
Due Date : The due date is a "no later than" date. That means you can turn it in earlier than Tuesday, December 6 at 2 pm but not later. If you are on your deathbed on Tuesday but alive on Wednesday, your project had better be in or you will receive a zero. No late homework passes can be used. No late projects accepted.
Theorems &
Postulates List:
1.
Three non-collinear points determine a plane.
2.
If two planes intersect, then their intersection is a line.
3.
Two points determine a line.
4.
If a line is tangent to a
radius at its outer endpoint then it is tangent to the circle.
5.
Vertical angles are congruent.
6.
All radii of a circle are
congruent.
7.
If two sides of a triangle
are congruent, then the angles opposite those sides are congruent.
8.
If two angles are both
supplementary and congruent, then they are right angles.
9.
If two angles of a triangle
are congruent, then the sides opposite those angles are congruent.
10. If two points are equidistant from the
endpoints of a segment, then the two endpoints determine the perpendicular bisector
of that segment.
11. If a point is on the perpendicular bisector of
a segment, then it is equidistant of a segment, then it is equidistant from the
endpoints.
12. If two non-vertical lines are parallel, then
their slopes are the same.
13. If a line is perpendicular to other coplanar lines
then then two other lines are parallel.
14. If two lines are cut by a transversal then the
alternating interior angles are congruent.
15. If two lines are cut by a transversal, then
the alternating exterior angles are congruent.
16. If two lines are cut by a transversal, then
the corresponding angles are congruent.
17. If two lines are cut by a transversal, then
the same side interior angles are supplementary.
18. In a plane, if a line is perpendicular to one
of two parallel lines, then it is perpendicular to the other.
19. A line and a point not on the line determine a
plane.
20. If two lines are parallel to a third line,
they are parallel to each other.
21. Two intersecting lines determine a plane.
22. Two parallel lines determine a plane.
23. If a radius is perpendicular to a chord then
it bisects the chord.
24. The
perpendicular bisector of a chord passes through the center.
25. If two chords of a circle are equidistant from
the center, then they are congruent.
26. If two tangent segments are drawn to a circle
from an external point, then those segments are congruent.
You may also choose from this list of shapes.
27. Circle
with an inscribed angle.
28. Internally tangent circles
29. Similar figures
30. Externally tangent circles
31. Circle with secants
32. Circle with a tangent
Have fun!
