Online Geometry: Angles, Theorems and Problems

Angles Theorems and Problems- Table of Content

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

Points, Theorems and Problems - Index.
Vertex.

Acute Angle in the Real World - Slideshow.

Obtuse Angle. Theorems and Problems.

Angles: 30, 60, 120 degrees.

Angles: 45, 135 degrees.

Angle Bisector.

Billiards and Geometry - Index
Angles of Incidence and Reflection.

Book I, Proposition 9: Bisect a given angle

Incenter. Index.
Angle bisectors.

Excenter. Index.
Interior and Exterior Angle bisectors.

PRK and Laser Eye Surgery.
The light rays, upon being transmitted through the lens, are refracted to an angle causing them to converge directly at the fovea, which is the area of the retina with the highest concentration of light sensitive cells.

Inca Stone of Twelve Angles, Cuzco. Tunnel effect.

Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem

Animated illustration of the celebrated Morley's angle trisector theorem 

Morley's Triangle & Center: Trisection of angles.

Blanchet Theorem. Altitude, Angle Bisector.

Isogonic-Jacobi Theorem: Using TracenPoche Dynamic Geometry Software

Mascheroni Construction with compass alone. Midpoint of a segment. Equal angles.

Interactive Simson Line. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Vertical angles.

Triangle: Incircle, Perpendicular, Angle Bisector. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.

Geometry Problem 715.
Triangle, Altitudes, Parallel, Circumcircle, Angle, Measurement.

Geometry Problem 707.
Triangle, Excenters, Angle Bisectors, Angle, Measurement.

Geometry Problem 698.
Quadrilateral, Diagonal, Angle Bisector, Triangle, 120 Degrees.

Geometry Problem 696.
Triangle, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Geometry Problem 695.
Triangle, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

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

Geometry Problem 691.
Isosceles Triangle, 80-80-20 Degrees, Angles, Congruence, 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 674.
Triangle, Altitude, Angles.

Geometry Problem 671.
Triangle, Cevian, Angles, Congruence.

Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles.

Geometry Problem 649.
Archimedes Book of Lemmas: Proposition 10
Tangent, Chord, Parallel, Midpoint.

Geometry Problem 648.
Archimedes Book of Lemmas: Proposition 9
Perpendicular chords, Arcs.

Geometry Problem 647.
Archimedes Book of Lemmas: Proposition 8
Angle trisection. Neusis construction.

Geometry Problem 620
Three Rectangles, Diagonals, Centers, Angles.

Problem 556.
Quadrilateral, Diagonal, Angles, Auxiliary Lines.

Proposed Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence.

Proposed Problem 424.
Triangle, Cevian, Angle, 90 degree, Congruence.

Proposed Problem 423.
Triangle, 30, 40 degree, Angle, Congruence.

Proposed Problem 422.
Triangle, 24, 30 degree, Angle, Congruence.

Proposed Problem 421.
Right Triangle, Cevian, Angles, Measurement.

Proposed Problem 420.
Triangle, Altitude, Angles, Sides, Measurement.

Proposed Problem 417.
Tangent circles, Tangent lines, Angles.

Proposed Problem 415.
Right Triangle, Cevian, Angles, Congruence.

Proposed Problem 414.
Triangle, Angles, Altitude, Median, Congruence.

Proposed Problem 412.
Triangle, Angles, Congruence.

Proposed Problem 411.
Triangle, Median, Angles.

Proposed Problem 410.
Two Regular Pentagons, Angle.

Proposed Problem 409.
Quadrilateral, Diagonals, Perpendicular, Congruence.

Proposed Problem 406.
Right triangle, 15 degrees, Midpoints, Congruence.

Proposed Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint.

Proposed Problem 383.
Concave Quadrilateral, Angle Bisectors, Semi-difference of Angles.

Proposed Problem 382.
Concave Quadrilateral, Angle Bisectors, Angles.

Proposed Problem 381.
Quadrilateral, Diagonals, Angle Bisectors, Angles.

Proposed Problem 377.
Triangle, Internal Angle Bisector, Altitude.

Proposed Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

Proposed Problem 375.
Triangle, Excenter, External Angle Bisectors.

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

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

Proposed Problem 363.
Right triangle, Congruence, Angles.

Proposed Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle.

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

Proposed Problem 354.
Rhombus, Square, 45 degrees.

Proposed Problem 350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles.

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

Proposed Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.

Proposed Problem 215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral.

Proposed Problem 208. Triangle, Excircles, Angles, 360 degrees.  

Proposed Problem 199. Triangle, Quadrilateral, Angles.

Proposed Problem 198. Triangle, Quadrilateral, Angles.

Proposed Problem 187. Right Triangle, Altitude, Incenters, Circles, Angles.  

Proposed Problem 185. Trapezoid, Triangles and Angles.  

Proposed Problem 184. Triangle and Angles.  

Proposed Problem 182. Overlapping Circles, Find an angle.  

Proposed Problem 181. Circular Sector of 90 degrees, find an angle.  

Proposed Problem 179. Rhombus, Square, Diagonal, Angle.  

Proposed Problem 134. Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter.  

Proposed Problem 133. Triangle, Angle Bisectors, Collinear Points.

Triangle with the bisectors of the exterior angles. Collinearity. Key concept: Menelaus Theorem.
 

Proposed Problem 128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.

Proposed Problem 127. Centroid and Incenter of a Triangle, Parallel, Proportions.

Proposed Problem 126. Incenter of Triangle, Angle Bisector, Proportions.

Proposed Problem 111. Orthogonal Circles (two circles that are perpendicular at their intersection).

Proposed Problem 109. Angles, Right Triangle, Cevian.

Proposed Problem 108. Angles, Triangle, Median.

Proposed Problem 107. Angles, Triangle. Cevian.

Proposed Problem 106. Angles, Triangle. Cevian.

Proposed Problem 105.Angles, Triangle. Interior Point.

Proposed Problem 104. Angles, Triangle.

Proposed Problem 101.Equilateral Triangle, Pythagorean Theorem, Angles.

Proposed Problem 1: Angles of a Triangle. Midpoint, Congruence. Hints are provided.

Proposed Problem 13: Angles of a Triangle. Hints are provided.

Proposed Problem 77: Angles of a Circle. Parallel lines, Cyclic quadrilateral.

Proposed Problem 74: Three Intersecting Circles. Cyclic quadrilateral, Angles.

Proposed Problem 73: Three Intersecting Circles. Cyclic quadrilateral. Angles.

Proposed Problem 72: Intersecting Circles. Cyclic quadrilateral, Chords, Parallel. Angles.

Proposed Problem 71: Cyclic Quadrilateral. Angles

Proposed Problem 67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
 

Proposed Problem 60: Isosceles triangle and angles.

Proposed Problem 57: Angle bisector, circles Cyclic Quadrilateral.

Proposed Problem 56: Angle bisector, circles Parallel Lines.

Proposed Problem 55: Angle bisector, circles Cyclic Quadrilateral.

Proposed Problem 54: Angle bisector, circles Midpoint of arc.

Proposed Problem 53: Angle bisector, circles

Proposed Problem 52: Triangle, angles, incircle.

Proposed Problem 50. Triangle with Equilateral triangles.
Seventeen conclusions. Angles

Proposed Problem 49. Angles and right triangle.

Proposed Problem 48. Angles and triangles.

Proposed Problem 47. Angles and triangles.

Proposed Problem 46. Angles and triangles.

Proposed Problem 45. Angles and triangles.

Proposed Problem 44. Angles and triangles.

Proposed Problem 43. Angles and triangles.

Proposed Problem 42. Angles and triangles.

Proposed Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances.

Proposed Problem 39.
Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles.

Proposed Problem 38.
Right Triangle, altitude, incircles, incenters, and angles.

Proposed Problem 37.
Right Triangle, altitude, incircles, incenters, orthocenter, and angles.

Proposed Problem 33.
Triangle and quadrilateral. Angles.

Geometry Test: Angles K-12

Geometry Online Glossary . Angles and more.
Geometry Glossary based on the new New York State mathematics standards initiative.