Presents interesting investigations and activities for inscribed and escribed circles of right-angled triangles. (ASK)

Previous work has identified four areas of difficulty that students seem to have with the topic of similarity: (1) understanding the definition of similarity; (2) proportional reasoning; (3) dimensional growth relationships; and (4) correspondences in right triangle similarity. This paper reports the results of an investigation into high school…

The concept of trigonometric ratios in a right triangle can be clearly presented through the use of interactive-geometry software. Investigation in this manner allows students to see the crucial features of the concepts before they are formalized and to gain ownership of these ideas through discovery. Many examples of the mathematical…

Provides an activity to develop students' (grade 5 through 10) spatial understanding and problem solving ability. Describes materials, prerequisites, directions, extensions, and technology using Geometric Supposer software. Presents worksheets and answers. Four references are listed. (YP)

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in geometry including Euclidean, post-Euclidean, and non-Euclidean geometry. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally…

Describes some general techniques for making collapsible models, including spiral models, for all the Platonic solids except the cube. Discusses the nature of the dissections of the faces necessary for the construction of the spiral cube. (ASK)

Considers the problem of how to go from three coordinates to two. States that it is not a problem that mathematics students ordinarily encounter. Presents four methods of graphing three-dimensional figures on a two-dimensional computer screen. (PK)

Reports evidence of construction and coordination of units in a measurement setting using data gathered from four students during individual problem-solving sessions near the end of their fourth-grade year. Proposes the task of measuring two-dimensional regions becomes possible when a student can construct two-dimensional units and coordinate…

Presents a unit to review geometric concepts and problem solving by having students work cooperatively to discover geometric shapes constructed from two congruent right triangles obtained from cutting a rectangle along its diagonal. Students report their findings both orally and in writing. (MDH)

Describes activities that use the geometric construction capabilities of the Geometer's Sketchpad computer software to explore triangles. Topics investigated include angle measurement, the sum of the measures of the angles of a triangle and a five-pointed star, triangle classification, and area and perimeter of a triangle. (MDH)

Shows how to construct a cube using Origami techniques. Also shows how, by identifying analogous features, to construct an octahedron. (JN)

Uses colored cube combinations to investigate surface area, volume, and axes of symmetry. (ASK)

Describes how origami can be used to help elementary school students learn geometrical concepts of shapes in two and three dimensions. Discusses equilateral triangles, Stars of David, rhombuses, and spirals. (MM)

Discusses the distinction between drawing and constructing in dynamic geometry environments. (MKR)

Explains how geometric constructions can enrich students' visualization and comprehension of geometry. Presents examples of geometric constructions that students can construct using the Geometer's Sketchpad. (ASK)