Morgan's Theorem
Tad Watanabe, Robert Hanson, and Frank D. Nowosielski
	Investigating the area of a hexagon formed in the interior of a triangle by certain n-	sectors of the angle.
	(889, 1996)  420 - 423

Using a Surface Triangle to Explore Curvature
James Casey
	Investigating triangle angle sums on various surfaces, e.g., bananas, soap bottles, 
	watermelons, etc.
	(87, 1994)  69 - 77

The Sidesplitting Story of the Midpoint Polygon
Y. David Gau and Lindsay A. Tartre
	The midline of a triangle theorem.  Varignon's theorem.  Extensions to pentagons 
	and other polygons.
	(87, 1994)  249 - 256

Golden Triangles, Pentagons, and Pentagrams
William A. Miller and Robert G. Clason
	Informal investigations of recursion.  The golden ratio, Fibonnaci sequence, regular 
	polygons, and pentagrams.
	(87, 1994)  338 - 344, 350 - 353

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

Heron's Remarkable Triangle Area Formula
Bernard M. Oliver
	Heron's proof and a modern short proof.  
	(86, 1993)   161 - 163

The Use of Dot Paper in Geometry Lessons
Ernest Woodward and Thomas Ray Hamel
	Area, perimeter, congruence, similarity, Cevians.  
	(86, 1993)    558 - 561

SSA and the Steiner-Lehmus Theorem
David Beran
	Conclusions which can be drawn from an SSA correspondence and a
	proof of the Steiner-Lehmus theorem.
	(85, 1992)    381 - 383

Area of a Triangle
Donald W. Stover
	Sharing Teaching Ideas.  An alternate method for finding the area of
	a triangle given the lengths of the sides.
	(83, 1990)  120

Why is the SSA Triangle Congruence Theorem Not Included in Textbooks?
Daniel B. Hirschhorn
	A plea for the inclusion of a special instance of SSA.
	(83, 1990)  358 - 361

SSA: The Ambiguous Case
Carolyn J. Case
	Sharing Teaching Ideas.  Presents a chart for investigating SSA.
	(82, 1989)     109 - 111

Triangles of Equal Area and Perimeter and Inscribed Circles
Jean E. Kilmer
	A triangle has equal area and perimeter if and only if it can be
	circumscribed about a circle of radius 2.
	(81, 1988)    65 - 70

Primitive Quadruples for the Law of Cosines
Mark A. Mettler
	Investigating a*a = b*b + c*c - 2bc cos A for A = 60, 90, 120 degrees.
	(81, 1988) 306 - 308

Reopening the Equilateral Triangle Problem: What Happens If . . .
Douglas L. Jones and Kenneth L. Shaw
	Investigations arising from a question about the sum of the distances
	from an interior point to the sides of an equilateral triangle.
	(81, 1988)    634 - 638

Let ABC Be Any Triangle
Baruch Schwartz and Maxim Bruckheimer
	Drawing a triangle that does not look special.
	(81, 1988)    640 - 642

The Peelle Triangle
Alan Lipp
	Information which can be deduced from the triangle about points, lines,
	segments, squares, and cubes.  A relation to Pascal's triangle.
	80, (1987)  56 - 60.

Two Views of Oz
John Pancari and John P. Pace
	Using the Scarecrow's Pythagorean-like utterance to define the
	fundamental isosceles triangle of Oz.
	80, (1987)  100 - 101.

Another Approach to the Ambiguous Case
Bernard S. Levine
	Using the law of cosines to set up a quadratic equation.
	80, (1987)  208 - 209.

A Geometric Proof of the Sum-Product Identities for Trigonometric Functions
Joscelyn Jarrett
	Utilizing points on a unit circle.
	80, (1987)  240 - 244.

Rethinking the Ambiguous Case
Allen L. Peek
	Again relating the solution of the problem to the solution of a
	quadratic equation.
	80, (1987)  372.

Illustrating the Euler Line
James M. Rubillo
	Finding the coordinates of the points on the line.
	80, (1987)  389 - 393.

Some Theorems Involving the Lengths of Segments in a Triangle
Donald R. Byrkit and Timothy L. Dixon
	Proof of a theorem concerning the length of an internal angle
	bisector in a triangle.  Other related results are included.
	80, (1987)  576 - 579.

Integer-sided Triangles and the SSA Ambiguity
Abraham M. Glicksman
	Some results concerning integer-sided triangles that contain a
	60-degree angle.
	80, (1987)  580 - 584.

Problem Solving in Geometry - a Sequence of Reuleaux Triangles
James R. Smart
	Investigation of area relations for a sequence of Reuleaux
	triangles associated with an equilateral triangle and a sequence
	of medial triangles.
	79, (1986)  11 - 14.

Did the Scarecrow Really Get A Brain?
Lowell Leake
	An analysis of the Scarecrow's Pythagoras-like statement in
	The Wizard of Oz.
	79, (1986)  438 - 439.

A Property of Right Triangles and Some Classical Relations
Angelo S. DiDomenico
	A Pythagorean triple relation which leads to other results including
	Heron's formula and the law of cosines.
	79, (1986)  640 - 643.

Drawing Altitudes of Triangles
Susan A. Brown
	Graph paper exercises to reinforce the definition.
	78, (1985)  182 - 183.

An "Ancient/Modern" Proof of Heron's Formula
William Dunham
	Utilizing Heron's inscribed circle and some trigonometric results.
	78, (1985)  258 - 259.

Investigating Shapes, Formulas, and Properties With LOGO
Daniel S. Yates
	Logo activities leading to results on areas and triangle geometry.
	78, (1985)  355 - 360.  (See correction p. 472.)

Triangles, Rectangles, and Parallelograms
Melfried Olsen and Judith Olsen
	Activities involving the manipulation of models of geometric figures.
	76, (1983)  112 - 116.

An Improvement on SSA Congruence for Geometry and Trigonometry
Shraga Yushurum and David C. Kay
	Conditions under which SSA yields congruence.  A result for
	non-Euclidean geometry is also presented.
	76, (1983)  364 - 367.

SSA: When Does It Yield Triangle Congruence?
Bonnie H. Litwiller and David R. Duncan
	One of three further conditions will guarantee the result.
	74, (1981)  106 - 108.

Area = Perimeter
Lee Markowitz
	When is the area of a triangle equal to its perimeter?
	74, (1981)  222 - 223.

Those Amazing Triangles
Christian R. Hirsch
	Activities.  Morley's triangle.  Outer Napoleon triangle.
	74, (1981)  444 - 448.

80 Proofs From Around The World
Tony Trono
	Proofs of "If the angle bisectors of a triangle are equal then
	the triangle is isosceles."
	74, (1981)  695 - 696.

The Golden Mean and An Intriguing Congruence Problem
David L. Pagini and Gerald E. Gannon
	Another approach to triangles which have five non-corresponding
	congruent parts but which are not congruent.
	74, (1981)  725 - 728.

Isosceles Triangles With The Same Perimeter and Area
Mark E. Bradley
	There can never be more than two isosceles triangles having a given
	number as both perimeter and area.
	73, (1980)  264 - 266.

Area and Cost Per Unit: An Application
Jan J. Vandever
	Activities for practice with area formulas.
	73, (1980)  281 - 284, 287.

Beyond The Usual Constructions
Melfried Olson
	Activities leading to the Fermat point, Simpson line, etc.
	73, (1980)  361 - 364.

Exploring Congruent Triangles
A. S. Green
	A suggested method for the introduction of congruence of triangles.
	73, (1980)  434 - 436.

Graphing - Perimeter - Area
Merrill A. Meneley
	Activities dealing with areas and perimeters of polygons.  Uses a
	coordinate system.
	73, (1980)  441 - 444.

Serendipity On The Area Of A Triangle
Madelaine Bates
	When are the area and the perimeter of a triangle equal?
	72, (1979)  273 - 275.

Right Or Not: A Triangle Investigation
Daniel T. Dolan
	Activities leading to the development of relations between the
	lengths of the sides of a triangle and its classification according
	to angle size.
	72, (1979)  279 - 282.

Pie Packing
William Jacob Bechem
	Activities for investigating properties of 30 - 60 and isosceles
	right triangles.
	72, (1979)  519 - 522.

Tiling
Richard A. Freitag
	Activities involving the replication of figures.  Congruence and
	similarity.
	71, (1978)  199 - 202.

Computer Classification Of Triangles and Quadrilaterals - A Challenging
Application
J. Richard Dennis
	Computer application, uses coordinates of vertices.
	71, (1978)  452 - 458.

Tetrahexes
Raymond E. Spaulding
	Activities involving congruence and symmetry.
	71, (1978)  598 - 602.

Problem Posing and Problem Solving: An Illustration Of Their Interdependence
Marion A. Walter and Stephen I. Brown
	Given two equilateral triangles, find a third whose area is the sum
	of the areas of the first two.  The Pythagorean Theorem and a
	generalization.
	70, (1977)  4 - 13.

The Key Duplicator: A Congruence Machine
Caroline Hollingsworth
	The relation of a key duplicator to congruence of geometric figures.
	70, (1977)  127 - 128.

Some Novel Consequences Of The Midline Theorem
Larry Hoehn
	Application of the theorem concerning the segment joining the midpoints
	of the sides of a triangle.
	70, (1977)  250 - 251.

Almost Congruent Triangles With Integral Sides
John T.F. Briggs
	Triangles having five parts of one congruent to five (non-corresponding)
	parts of the other.
	70, (1977)  253 - 257.

An Investigation Of Integral 60  and 120  Triangles
Richard C. Muller
	Law of cosines investigation.  Computer related.
	70, (1977)  315 - 318.

Notes On The Partial Converses Of A Familiar Theorem
William M. Waters, Jr.
	Partial converses of the result that for an isosceles triangle the
	bisector of the apex angle, the altitude to the base and the median
	to the base are identical.
	70, (1977)  458 - 460.

Congruence Extended: A Setting For Activity In Geometry
Gail Spittler and Marian Weinstein
	Special (two part) triangle congruence theorems.  Quadrilateral
	congruence theorems.
	69, (976)  18 - 21.

Some Additional Results Involving Congruence Of Triangles
Norbert J. Kuenzi, John A. Oman, and Robert W. Prielipp.
	Some congruence results involving area and perimeter.
	68, (1975)  282 - 283.

A New Look At The "Center" Of A Triangle
James E. Lightner
	An approach to problems associated with medians, altitudes, and angle
	bisectors of a triangle.
	68, (1975)  612 - 615.

The Converses Of A Familiar Isosceles Triangle Theorem,
F. Nicholson Moore and Donald R. Byrkit
	Converses, the difference between necessary and sufficient conditions,
	use of counterexamples.
	67, (1974)  167 - 170.

Are Triangles That Have The Same Area and The Same Perimeter Congruent?
Robert W. Prielipp
	Some theorems about right triangles and a counterexample.
	67, (1974)  157 - 159.

More About Triangles With The Same Area and The Same Perimeter
Donavan R. Lichtenberg
	Device for decomposing a triangle with a given area and perimeter into
	another having the same area and the same perimeter.
	67, (1974)  659 - 660.

In Search Of The Perfect Scalene Triangle
Bro. L. Raphael, F.S.C.
	Drawing a triangle which is noticeably not isosceles nor right.
	66, (1973)  57 - 60.

A Generalization Of Vux Triangles
Charles Brumfiel
	A vux triangle has one angle double another.  Here we consider one
	angle k times another.
	65, (1972)  171 - 174.

Using The Laboratory Approach To Relate Physical and Abstract Geometry
Nancy C. Whitman
	Activities involving the segment determined by the midpoints of
	two sides of a triangle.
	65, (1972)  187 - 189.

The Three-Point Problem
A. Day Bradley
	Given a triangle ABC and the angles subtended by the sides of the
	triangle at a point D in the same plane, find the distances DA, DB, and
	DC.  (The problem of Pothenot.)
	65, (1972) 703 - 705.

An Old Stumbling Stone Revisited
Robert R. Poole
	Trigonometry applied to the angle bisectors of an isosceles triangle.
	63, (1970)  259.

Vux Triangles
Fitch Cheney
	Triangles in which one angle is double another.
	63, (1970)  407 - 410.

A Project In Mathematics
J. Garfunkel
	Ten problems involving products of lengths of Cevians.
	61, (1968)  243 - 248.

5 - Con Triangles
Richard G. Pawley
	Triangles having five parts of one congruent to five (non-corresponding)
	parts of the other.
	60, (1967)  438 - 443.

Congruency Of Triangles By AAS
Don Ryoti
	Two proofs of the theorem.
	59, (1966)  246 - 247.

A Scale For "Scaleneness"
Evelyn B. Rosenthal
	Uses  (perimeter - squared)/area  to establish a ranking.
	58, (1965)  318 - 320.

A Dialogue On Two Triangles
Leander W. Smith
	When will the perimeter and the area of a triangle be numerically equal?
	57, (1964)  233 - 234.

Dr. Hopkins' Proof Of The Angle Bisector Problems
Sister Mary Constantia, S.C.L.
	A direct proof of the result that if two angle bisectors are congruent
	the triangle is isosceles.
	57, (1964)  539 - 541.

Altitudes, Medians, Angle Bisectors and Perpendicular Bisectors Of The
Sides Of A Triangle
Harry Schor
	Paper folding.
	56, (1963)  105 - 106.

The Problem Of The Angle Bisector
Joseph Holzinger
	If two angle bisectors of a triangle are congruent the triangle is
	isosceles.  The result is trigonometrically based.
	56, (1963)  321 - 322.

Notes On The Centroid
Nathan Altshiller Court
	Primarily historic.
	53, (1960)  33 - 35.

The Use Of Congruence In Geometric Proofs
Carl Bergman
	Using directed triangles in congruence proofs.
	51, (1958)  23 - 26.

Micky's Proof Of The Medians Theorem
M. L. Keedy
	Using informal deduction to prove that the medians of an isosceles
	triangle are congruent.
	51, (1958)  453 - 455.

Congruent Triangles (Fifth Case) and The Theorem Of Lehmus
Victor Thebault
	A proof of a congruence theorem concerning angle bisectors.
	48, (1955)  97 - 98.

On Certain Cases Of Congruence Of Triangles
Victor Thebault
	Congruence theorems related to division ratios.
	48, (1955)  341 - 343.

Quasi-Right Triangles
Adrian Struyk
	Triangles such that the difference of two angles is 90 degrees.
	47, (1954)  116 - 118.

More Than Similar Triangles
Charles Salkind
	Triangles such that five parts of one are congruent to five
	(non-corresponding) parts of the other.
	47, (1954) 561 - 562.

A New Proof Of An Old Theorem
Francis A. C. Sevier
	Deals with the angle bisectors of an isosceles triangle.
	45, (1952)  121 - 122.

Relations For Radii Of Circles Associated With The Triangle
T. Freitag
	Circumradius, inradius, etc.
	45, (1952)  357 - 360.

Signed Areas Applied To "Recreations Of Geometry"
H.C. Trimble
	Analytic approach to some triangle geometry.  Danger in arguing from
	a figure.
	40, (1947)  3 - 7.

Escribed Circles
Joseph A. Nyberg
	Geometry of the circles.
	40, (1947)  68 - 70.

Dynamic Geometry
John F. Schact and John J. Kinsella
	The use of triangle and quadrilateral linkages as teaching devices.
	Some circle geometry.
	40, (1947)  151 - 157.

A New Technique In Handling The Congruence Theorems In Plane Geometry
Ralph C. Miller
	Using constructions.
	36, (1943)  237 - 239.

The Congruence Theorems By A New Proof
H.C. Christofferson
	The use of an assumption which enables one to avoid the use
	of superposition.
	28, (1935)  223 - 227.

Assuming The Congruence Theorems
Joseph A. Nyberg
	What should be assumed and what should be proved?
	24, (1931)  395 - 399.

Proving The Equality Of The Base Angles Of An Isosceles Triangle
Joseph A. Nyberg
	Need we assume the existence of an angle bisector?
	22, (1929)  318 - 319.

Isotomic Points Of The Triangle
Richard Morris
	Isotomic points, Gergonne points, Nagel points.
	21, (1928)  163 - 170.

Circles Through Notable Points Of The Triangle
Richard Morris
	Circles through three, four, five, and six points.
	21, (1928)  63 - 71.

Proof Of An Original Exercise
Walter Beyer
	On the sides of a triangle ABC construct equilateral triangles AEC, CDB,
	and BFA.  Show that AD, BE, and CF are concurrent.
	20, (1927)  91 - 92.

Interesting Work Of Young Geometers
J. T. Rorer
	Three triangle theorems and an approximate trisection.
	1, (1908-1909)  147 - 149.

H.J.L.
07/15/97
email:  00hjludwig@bsu.edu
home page: http://www.cs.bsu.edu/~hjludwig/