The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)

The activities are designed to have students manipulate physical models of geometric figures, engage in spatial visualization and observe relationships between triangles and parallelograms and between triangles and rectangles. Worksheets designed for duplication are included in the materials and an answer key is provided. (MP)

Worksheets are provided for use by students in grades 8 and above when sectioning a tetrahedron. Lesson objectives include the discovery of generalizations regarding the cross-sections of a tetrahedron. (MK)

Summarizes and extends a well-known geometry theorem that states that any triangle inscribed in a circle with one side of the triangle a diameter of the circle, is a right triangle. (ASK)

Archimedes viewed the method of centroids as a valuable tool for intuitive discoveries. This article presents several uses of this technique and discusses how the method of centroids could be used in secondary schools. (Author/MK)

A system of area measurement developed for the isometric geoboard is used to justify some relationships that are often proved using square units of area. (Author/MK)

Examples are given of computer activities in analytic geometry. (MK)

A question posed by Euler is considered: How can polyhedra be classified so that the results is in some way analogous to the simple classification of polygons according to the number of their sides? (MK)

Activities designed to lead pupils through the process of using the basic measuring and drawing devices of geometry are presented and move to the discovery of several surprising generalizations about arbitrary triangles. (MP)

Presents Heron's original geometric proof to his formula to calculate the area of a triangle. Attempts to improve on this proof by supplying a chain of reasoning that leads quickly from premises to the conclusion. (MDH)

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…

Children's perception and understanding of three-dimensional figures and of operations on them is discussed. Piaget's findings are reviewed and more current research is described. Classroom implications are explored. (SD)

Relationships among the sides are developed for right triangles whose sides are in the ratios 1:3, 1:4, and 1:5. The golden ratio appears in the results which can be used in secondary mathematics. (DC)

Provides a proof that, if two angle bisectors of a triangle are equal in length, the triangle is isosceles (Steiner-Lehmus Theorem) using two corollaries related to a side-side-angle correspondence in a triangle. Introduces historical developments in the discussion of the proof. (MDH)

Paper-folding activities demonstrate properties of the conic sections and equilateral triangles. (SD)