### Mathematics Teacher

#### Geometry Bibliography: Quadrilaterals

Hubert Ludwig, Ball State University

 ```Trap a Surprise in an Isosceles Trapezoid Margaret M. Housinger Isosceles trapezoids with integral sides in which a circle can be inscribed. (889, 1996) 12 - 14 Theorems in Motion: Using Dynamic Geometry to Gain Fresh Insights Daniel P. Scher Construction of a constant-perimeter rectangle; a constant area rectangle. (889, 1996) 330 - 332 Concept Worksheet: An Important Tool for Learning Charalampos Toumasis The example presented is geometric in nature, it deals with the characterization of a parallelogram. (88, 1995) 98 - 100 When Is a Quadrilateral a Parallelogram? Charalampos Toumasis Investigations of sets of sufficient conditions. (87, 1994) 208 - 211 Creative Teaching Will Produce Creative Students Stephen Krulik and Jess A. Rudnick Solving the problem of finding all rectangles with integral dimensions whose area and perimeter are numerically equal. (87, 1994) 415 - 418 Counting Embedded Figures Timothy V. Craine Activities. How many triangles, squares, rectangles, etc., are there in a given figure? (87, 1994) 524 - 528, 538 - 541 A Quadrilateral Hierarchy to Facilitate Learning in Geometry Timothy V. Craine and Rheta N. Rubenstein Creating a "family tree" for quadrilaterals to enable generalization of results. Analytic proofs are also involved. (86,1993) 30 - 36 Ladders and Saws Debra Tvrdik and David Blum An activity for demonstrating many geometric relationships from angle sums of polygons to properties of parallelograms. (86, 1993) 510 - 513 Improving Students' Understanding of Geometric Definitions Jim Hersberger and Gary Talsma Sharing Teaching Ideas. Activities involving standard convex quadrilaterals. (84, 1991) 192 - 194 Area Ratios of Quadrilaterals David R. Anderson and Michael J. Arcidiacono Looks at the area of the quadrilateral formed by joining points on the sides of a given quadrilateral. (82, 1989) 176 - 184 An Application of the Criteria ASASA for Quadrilaterals Spencer P. Hurd A series of results leading to the Theorem of Pythagoras. (81, 1988) 124 - 126 Discoveries with Rectangles and Rectangular Solids Lyle R. Smith Differentiating between area and perimeter for rectangles and between volume and surface area for rectangular solids. 80, (1987) 274 - 276. Geometrical Adventures in Functionland Rina Hershkowitz, Abraham Arcavi, and Theodore Eisenberg Determining the change in area produced by making a change in some property of a particular figure. 80, (1987) 346 - 352. Median of a Trapezoid Pamela Allison Using the result about the segment joining the midpoints of the sides of a triangle in order to find the length of the median of a trapezoid. 79, (1986) 103 - 104. A Postal Scale Linkage Andrew A. Zucker A "Sharing Teaching Idea". Use of physical models. Application to quadrilaterals. 78, (1985) 431 - 43 The Rhombus Construction Company Joseph A. Troccolo Activities for looking at properties of a rhombus. 76, (1983) 37 - 41. Triangles, Rectangles, and Parallelograms Melfried Olsen and Judith Olsen Activities involving the manipulation of models of geometric figures. 76, (1983) 112 - 116. President Garfield's Configuration Allan Weiner Geometric and trigonometric results derived from the trapezoidal configuration used by Garfield in his proof of the theorem of Pythagoras. 75, (1982) 567 - 570. Spirolaterals Richard Brannan and Scott McFadden Activities involving figures made up of rectangles on a grid. 74, (1981) 279 - 282, 285. Measuring Squares To Prepare For Pi Don E. Ryote Seven activities leading to a consideration of the ratio of perimeter to diagonal for a rectangle. 74, (1981) 375 - 379. Properties Of Quadrilaterals Stephen Maraldo Definitions, theorems, and a diagram. 73, (1980) 38 - 39. Area and Cost Per Unit: An Application Jan J. Vandever Activities providing practice with area formulas. 73, (1980) 281 - 284, 287. Are Circumscribable Quadrilaterals Always Inscribable? Joseph Shin A condition under which they will be is developed. 73, (1980) 371 - 372. Graphing - Perimeter - Area Merrill H. Murphy Activities concerning areas and perimeters of polygons. A coordinate system is used 73, (1980) 441 - 444. Computer Classification Of Triangles and Quadrilaterals - A Challenging Application J. Richard Dennis Computer application, uses coordinates of vertices. 71, (1978) 452 - 458. Exploring Skewsquares Alten T. Olson Properties of quadrilaterals having congruent, mutually perpendicular diagonals. (Transformational approach.) 69, (1976) 570 - 573. Consistent Classification Of Geometric Figures Joe K. Smith Suggestions for developing classification systems. 69, (1976) 574 - 576. Midpoints and Quadrilaterals W.J. Masalski Activities for considering what happens when figures are formed from polygons by using midpoints of segments. 68, (1975) 37 - 44. The Area Of A Parallelogram Is The Product Of Its Sides William J. Lepowsky An experiment concerning the area of a parallelogram. 67, (1974) 419 - 421. An Absent-Minded Professor Builds A Kite Norman Gore and Sidney Penner Can you build a trapezoid having the same side lengths as those of a kite? 66, (1973) 184 - 185. Midpoints and Measures L. Carey Bolster Activities involving figures formed using midpoints of sides of triangles and quadrilaterals. 66, (1973) 627 - 630. Urquhart's Quadrilateral Theorem Howard Grossman A proof and a generalization. 66, (1973) 643 - 644. Problem Solving In Geometry Arthur A. Hiatt Quadrilaterals formed by using trisection points of the sides of a quadrilateral. 65, (1972) 595 - 600. That Area Problem Benjamin Greenberg Finding the area of a quadrilateral formed by using trisection points of the sides of a quadrilateral. 64, (1971) 79 - 80. Some Results On Quadrilaterals With Perpendicular Diagonals Steven Szabo Characterization of such quadrilaterals, uses vector techniques. 60, (1967) 336 - 338. The N-Sectors Of The Angles Of A Square James R. Smart Extension of the concepts involved in Morley's theorem. 60, (1967) 459 - 463. What Is A Trapezoid? David L. Dye Is a parallelogram a trapezoid? 60, (1967) 727 - 728. What Is An Isosceles Trapezoid? Don E. Ryoti Is a parallelogram an isosceles trapezoid? 60, (1967) 729 - 730. What Is A Quadrilateral? Denis Crawforth Reprint from Mathematics Teaching. Activities concerning four points. 60, (1967) 778 - 781. What Is A Trapezoid? M. L. Keedy A parallelogram should be a trapezoid. 59, (1966) 646. A Unit In High School Geometry Without The Textbook Paul W. Avers Application of discovery methods to the study of quadrilaterals. 57, (1964) 139 - 142. Discovering The Centroid Of A Quadrilateral By Construction Samuel Kaner With a suggestion for generalization. 57, (1964) 484 - 485. Optional Proofs Of Theorems In Plane Geometry Francis G. Lankford, Jr. Parallels, angle sum of a triangle. 48, (1955) 578 - 580. Parallelogram and Parallelepiped Victor Thebault Theorems concerning diagonals. 47, (1954) 266 - 267. A Skew Quadrilateral Mathematics Laboratory (Monroe High School) Construction of a model. 46, (1953) 50 - 51. A Parallelogram Device M. H. Ahrendt The construction and uses of a linkage. 43, (1950) 350 - 351. Functional Thinking In Geometry Hale Pickett Some results concerning the consequences of joining the midpoints of the sides of a quadrilateral. 33, (1940) 69 - 72. The Story Of The Parallelogram Robert C. Yates Parallelograms and linkages. 33, (1940) 301 - 309. H.J.L. 07/15/97 email: 00hjludwig@bsu.edu home page: http://www.cs.bsu.edu/~hjludwig/ ```

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