Geogebra  "4th hour"

## Assignments Spring, 2016

Software:   GeoGebra.

TEXTS for Math 371:

•  Fundamentals of Geometry by B.Meserve and J. Izzo, A.W. (1969) - ON LINE  through Moodle.
• The Elements by Euclid, Volume 1, edited by T.L. Heath, Dover (1926)
• The Elements (David Joyce's on-line version)
The First Six Books of The Elements of Euclid (Comprehensive connections with Oliver Byrne's on-line version)
• Proof in Geometry by A.I Fetisov, Mir (1978)
• Flatland, (one of many on-line versions available) by Edwin A. Abbott, Dover.

 Week Class Topic Class Tasks 1 1-27 Introduction to geometry technology. Points, lines, circles, intersections, figures, labels, and text. Introduction to GeoGebra. 2  2-3 More on points, lines, and using GeoGebra on-line. Special points. Special Lines. Download File from GeoGebra Tube Examine File. Construct a sketch with technology of  1. Euclid's Proposition 1 in Book I. 3 2-10 How to determine circles and arcs.Determining points and lines. Constructions: Points, lines, circles. 2. Euclid's Proposition 2 in Book I.  3. One "proof" of the Pythagorean Theorem. Do Construction 3, 4, 6, 7, and 8 from Meserve and Izzo Section 1.2. BONUS:Show how to "add" two arbitrary triangles to create a single square. 4 2-17 Transformations that preserve distance: Translations, Rotations, Reflections, Glide Reflections. 1. Construct a scalene triangle . Illustrate how to do i) a translation by a given "vector", ii) a rotation 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 5  2-24 Measurements. Central Similarities. Other Magnifications. Parameters(?) / Slider Problem 1 now due 2/22 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. 6  3-2 Rotations of lines about the point of intersection. 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 is 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  3-9 Draw sketches for each of the following triangle coincidences: 1. Medians. 2. Angle Bisectors. 3. Altitudes. 4. Perpendicular Bisectors Spring break 8  3-23 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