TEXTS for Math 371:
Assignments: Subject to Change.
Assignments are not made until a due date is established.
|1||Introduction to geometry technology. Points,
lines, circles, intersections, figures, labels, and text.
||Introduction to Technology for Geometry: Wingeometry, The Geometer's Sketchpad®, and GeoGebra.|
|2 Lab Exercises 1:
|More on points, lines, and circles.
||Construct a sketch with technology of
1. Euclid's Proposition 1 in Book I.
2. Euclid's Proposition 2 in Book I.
3. One "proof" of the Pythagorean Theorem.
|3 Lab Exercises 2:
||Constructions: Points, lines, circles.
||Do Construction 3, 4, 6, 7, and 8 from
and Izzo Section 1.2.
BONUS:Show how to "add" two arbitrary triangles to create a single square.
|4Lab Exercises 3:
||Transformations that preserve distance:
Translations, Rotations, Reflections, Glide Reflections.
|1. Construct a scalene
Illustrate how to do i) a translation by a given "vector", ii) a
by a given angle measure, and iii) reflections across a given line..
2. Create a sketch that shows that the product of two reflections is either a translation or a rotation
|5Lab Exercises 4:
Central Similarities. Other Magnifications.
Parameters(?) / Slider
1. Draw a figure showing the product of three planar reflections as a glide reflection.
2. Draw a figure illustrating the effects of a central similarity on a triangle using magnification or dilation that is a) positive number >1, b) a positive number <1, and c) a negative number.
|6Lab Exercises 5:
||Rotations of lines about the point of
More on use of angle measurements and perpendicular lines.
| 1. Construct the inverse
of a point with respect
to a circle a) when the point is inside the circle; b) when the point
outside the circle.
2. Given a circle O and two interior points A and B, construct an orthogonal circle O' through A and B.
3. Draw two intersecting circles O and O' and measure the angle between them.
|7 Lab Exercise 6:
||Draw sketches for each of
the following triangle
1. Medians. 2. Angle Bisectors. 3. Altitudes. 4. Perpendicular Bisectors
|8Lab Exercise 7:||1. Inversion: Investigate and sketch the result
of inversion on lines
and circles in the plane with a given circle for inversion.
When does a line invert to a line? When does a line invert to a circle? When does a circle invert to a line? when does a circle invert to a circle? Show sketches where each case occurs. [ Remember the inverse of the inverse is the original figure.]
2. Use inversion with respect to the circle OP to invert <BAC to <B'A'C'. Discuss briefly the effects of inversion on angles.
||Draw a sketch of the affine plane showing the horizon line and label the lines X=1,2,-1, Y= 1,2,-1 and points (1,2) and (2,-1).|
|10Lab Exercise 9:
features, draw a parabola, ellipse and hyperbola from focus
2. Use built in features of software to draw a parabola, ellipse and hyperbola from focus (and directrix).
|11Lab Exercise||A.1. Construct a sketch showing ABC on a line
perspectively related to
A'B'C' on a second line with center O.
2. Construct a sketch of ABC on a line projectively (but not perspectively) related to A'B'C' on a second line. Show two centers and an intermediate line that gives the projectivity.
B.1'. Draw a dual sketch for the figure in problem 1. 2'. Draw a dual sketch for the figure in problem 2.
C. Draw a sketch for Desargues' theorem in the plane.
configuration: Hexagons inscribed
in conics. Points of intersections of opposite sides lie on a single
Construct a figure for Pascal's configuration with a) an ellipse , b)a parabola, and c) an hyperbola.
|13Lab Exercise||A. Draw a figure in space that illustrates
the "conic sections".
B. Draw a spatial sketch for Desargues' Theorem
|14Lab Exercise||1.Draw a sketch showing H(AB,CD) and H(CD, AB) are equivalent. [Proof.]
2. Draw a sketch that shows that if H(AB,CD) and H(AB,CD*) then D= D*.[Proof.]