Isosceles Triangle, Theorems and Problems - Table of Content

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Euclid's Elements Book I, Proposition 5: (Pons Asinorum) Isosceles triangles

Isosceles Triangle 80-20-80. Index.

Perpendicular Bisector.

Triangle with Double Angle, Theorems and Problems, Index
 

Langley's Problem Adventitious angles. 20° isosceles triangle with animation.
 

Geometry Problem 874
Isosceles Triangle, Circumcircle, Circumcenter, Congruence.

Geometry Problem 867
Isosceles Triangle, Median, Perpendicular, Angle, Congruence.

Geometry Problem 859
Isosceles Right Triangle, Angles,18, 45 Degrees, Congruence, Perpendicular bisector.

Geometry Problem 858
Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence, Angles, Auxiliary Lines.

Geometry Problem 835
Isosceles Triangle, Double Angle, Triple Angle, Auxiliary Lines.

Geometry Problem 797
Parallelogram, Angle Bisector, Isosceles and Similar Triangles.

Geometry Problem 770
Parallelogram, Angle Bisector, Triangle, Circumcenter, Circumcircle, Angle Measurement.

Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence.

Geometry Problem 762
Parallelogram, Midpoint, Perpendicular, Congruence, Isosceles triangle.

Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations.

Geometry Problem 740.
Scalene Triangle, Angle, Semi-sum, Cevian, Isosceles Triangle.

Geometry Problem 739.
Triangle, Double Angle, External Angle Bisector. Congruence.

Geometry Problem 734.
Triangle, Isosceles, Median, Parallel, Angle Bisector, Congruence, Midpoint.

Geometry Problem 728.
Triangle, Altitude, Perpendicular, Circumcircle, Midpoint, Intersecting Circles, Concurrency.

Geometry Problem 727.
Triangle, Isosceles, Congruence, Angles, Measurement.

Geometry Problem 726.
Isosceles Triangle, Perpendicular, Midpoint, 90 Degrees.

Geometry Problem 694.
Triangle, Angles, 30 Degrees, Auxiliary Construction, Mind Map, Polya.

Geometry Problem 688.
Triangle, Angles, 10, 20, 30, 40, 60 Degrees, Measure, Mind Map, Polya.

Geometry Problem 685
Isosceles Triangle, 100-40-40 Degrees, Angles, Congruence.

Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines.

Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points.

Problem 577.
Isosceles triangle, Midpoint, Perpendicular, Concyclic points, Circle.

Proposed Problem 469.
Isosceles triangle, Midpoint, Transversal, Congruence.

Proposed Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle.

Proposed Problem 419.
Isosceles triangle, Cevian, Incircle, Excircle, Inradius, Exradius.

Proposed Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence,
Isosceles triangle.

Proposed Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence,
Isosceles triangle.

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence,
Isosceles triangle.

Proposed Problem 372.
Circles, Common Internal and External Tangent, Angles.
Isosceles triangle.

Proposed Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence.

Proposed Problem 274.
Isosceles Triangle, 80-80-20, Angles.

Proposed Problem 224. Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base.

Proposed Problem 223. Viviani's theorem, Isosceles triangle, Altitude, Distances.

Bottema's Theorem.
Invariance of an isosceles right triangle.
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

Kurschak's Tile and Theorem. Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric way of finding the area of a regular dodecagon.
32 congruent isosceles triangles.

Proposed Problem 325.
Isosceles triangle, Altitude, Cevian, Incircle, Excircle.

Mascheroni Construction with compass alone. Midpoint of a segment
Based on similarity of isosceles triangles.

Proposed Problem 252.
Rectangle, isosceles right triangle, square, area.

Proposed Problem 60: Isosceles triangle

Geometry Online Glossary . Isosceles triangle
Geometry Glossary based on the new New York State mathematics standards initiative.

MindMap of Euclid's Elements Book I
Triangles by Side: Equilateral, Isosceles, Scalene. 

Humans Hard-wired into brain for Geometry.
The Munduruku subjects, tested by a native speaker of Munduruku working with a linguist, were asked to identify the image that was ‘weird’ or ‘ugly.’ For example, to test the concept of right angles, a slide shows five right triangles and one isosceles triangle. The isosceles triangle is the correct answer.

Problem 19. Isosceles Right triangle, perpendicular, and Excenter.

Proposed Problem 13. Triangle, cevian, equal segments, and angles.
Auxiliary construction: Isosceles triangle.

Proposed Problem 2. Triangle and angles..
Auxiliary construction: Isosceles triangle.