Geometry: Angles 30°, 60°, 90°, 120°, Theorems and Problems

Angles 30°, 60°, 120° Index illustration
Geometry Problem 1610: Area of a Curvilinear Triangle in a Rhombus

Geometry Problem 1610: Area of a Curvilinear Triangle in a Rhombus

Geometry Problem 1586: Three Equilateral Triangles

Geometry Problem 1586: Unveiling a Unique Area Relationship in Three Equilateral Triangles

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Geometry Problem 1580: Triangle with 60 degrees

Geometry Problem 1580: 60-Degree Triangle Challenge: Uncover AD Using Excenter and Circumcircle Clues.

Geometry Problem 1566: Equilateral Triangle with Cevians

Geometry Problem 1566: Demonstrate AC Equals AE + CD in an Equilateral Triangle ABC Involving Cevians and 60 Degrees.

Geometry Problem 1496: Triangle with Double Angle

Geometry Problem 1496

Triangle, Congruence, Isosceles, Double Angle, 30 Degrees.

Geometry Problem 1495: Circle with Parallel Chords

Geometry Problem 1495

Circle, Parallel Chords, 30 Degree Angle, Radius Squared.

Geometry Problem 1433: Tangent Circles

Geometry Problem 1433

Tangent Circles, Diameter, Perpendicular, Midpoint, Measurement, Poster Typography, iPad Apps.

Geometry Problem 1429: Triangle with Median

Geometry Problem 1429

Triangle, Median, 15-30 degree, Angle, Congruence.

Geometry Problem 1356: Triangle with 30 degrees

Geometry Problem 1356

Quadrilateral, Triangle, Angle, 30 Degrees, Congruence.

Geometry Problem 1353: Tangent Circles

Geometry Problem 1353

Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees.

Geometry Problem 1346: Equilateral Triangle with Incircle

Geometry Problem 1346

Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance.

Geometry Problem 1345: Three Equilateral Triangles

Geometry Problem 1345

Three Equilateral Triangles, Center, Area, Common Vertex.

Geometry Problem 1323: Square with Equilateral Triangle

Geometry Problem 1323

Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 30-60 degrees.

Geometry Problem 1304: Triangle with 120 degrees

Geometry Problem 1304

Triangle, 120 Degrees, Angle Bisector, Measurement.

Geometry Problem 1303: Triangle with 60 degrees

Geometry Problem 1303

Triangle, 60 Degrees, Angle Bisector, Measurement.

Geometry Problem 1299: Triangles with Interior Point

Geometry Problem 1299

Triangles, Interior Point, Angles, 30 degrees.

Geometry Problem 1288: Triangle with 50-100 degrees

Geometry Problem 1288

Triangle, 30-50-100 Degrees, Area, Inradius, Metric Relations, Measurement.

Geometry Problem 1286: Quadrilateral with angles 60, 135, 105 degrees

Geometry Problem 1286

Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement.

Geometry Problem 1285: Quadrilateral with angles 60, 150, 90 degrees

Geometry Problem 1285

Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement.

Geometry Problem 1238: Square with Equilateral Triangle

Geometry Problem 1238

Square, Equilateral Triangle, Metric Relations. Mobile Apps.

Geometry Problem 1234: Quadrilateral with 60 degrees

Geometry Problem 1234

Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 1230: Quadrilateral with Equilateral Triangle

Geometry Problem 1230

Quadrilateral, 60 Degrees, Congruence, Metric Relations.

Geometry Problem 1225: Equilateral Triangle with Bisector

Geometry Problem 1225

Equilateral Triangle, Circumcircle, Angle Bisector, Congruence.

Geometry Problem 1222: Doubling the Cube

Geometry Problem 1222

Doubling the Cube, Triangle, 90, 120 degrees, Perpendicular, Congruence.

Geometry Problem 1220: Scalene and Equilateral Triangles

Geometry Problem 1220

Equilateral Triangles, Midpoints, 60 Degrees, Congruence.

Geometry Problem 1219: Equilateral Triangles and Rhombus

Geometry Problem 1219

Equilateral Triangles, Midpoints, 60 Degrees, Congruence, Rhombus.

Geometry Problem 1218: Scalene and Equilateral Triangles

Geometry Problem 1218

Scalene Triangle, Equilateral Triangles, Midpoints, 60 Degrees, Congruence.

Geometry Problem 1180: Quadrilateral with 120 degrees

Geometry Problem 1180

Quadrilateral, 120 Degrees, Diagonals, Perpendicular.

Geometry Problem 1161: Scalene Triangle with 60 degrees

Geometry Problem 1161

Scalene Triangle, 60 Degrees, Angle, Orthocenter, Circumcenter, Equilateral Triangle, Congruence.

Geometry Problem 1120: Isosceles Right Triangle

Geometry Problem 1120

Isosceles Right Triangle, 120 Degree, Angle, Equilateral, Metric Relations.

Geometry Problem 1062: Scalene Triangle with 60 degrees

Geometry Problem 1062

Scalene Triangle with an angle of 60 degrees, Euler Line, Orthocenter, Circumcenter, Distance, Congruence, Transversal.

Geometry Problem 1000: Triangle with 120 degrees

Geometry Problem 1000

Scalene Triangle, Isosceles, Angle, 120 Degree, Midpoint, Distance, Equilateral, Congruence, Perpendicular, Metric Relations.

Geometry Problem 992: Triangle with Interior Point

Geometry Problem 992

Triangle, Interior Point, Angles, 20, 30, 40, 50 Degree.

Geometry Problem 988: Right Triangle with Cevians

Geometry Problem 988

Right Triangle, Cevians, Angles, 30 Degrees, Triple Angle.

Geometry Problem 964: Right Triangle with Cevians

Geometry Problem 964

Right Triangle, Cevians, Angles, 10, 20, 30 Degrees.

Geometry Problem 956: Two Equilateral Triangles

Geometry Problem 956

Two Equilateral Triangles, Center, Collinear Points, Midpoint, Right Triangle, 30, 60, 90 Degrees.

Geometry Problem 894: Triangle with Incenter

Geometry Problem 894

Triangle, Angle, 60 degrees, Incenter, Midpoint, Parallel Lines.
GeoGebra, HTML5 Animation for Tablets

iPad Apps: Isometric

iPad Apps: Isometric

Hexagons, Rhombus 60-120 degrees.

Geometry Problem 892: Triangle with Orthocenter and Circumcenter

Geometry Problem 892

Triangle, 60 degrees, Orthocenter, Circumcenter.

Geometry Problem 872: Quadrilateral and Triangle

Geometry Problem 872

Quadrilateral, Triangle, Angle, 30, 90 degrees.

Geometry Problem 857: Triangle with Median

Geometry Problem 857

Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines.

Geometry Problem 856: Quadrilateral with Diagonal

Geometry Problem 856

Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Geometry Problem 855: Triangle with 30 degrees

Geometry Problem 855

Quadrilateral, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Geometry Problem 831: Quadrilateral with Diagonal

Geometry Problem 831

Quadrilateral, Diagonal, Midpoint, Opposite Angles, Congruence, Parallelogram.

Geometry Problem 830: Triangle and Quadrilateral

Geometry Problem 830

Quadrilateral, Triangle, Angles, 30 degrees, Congruence.

Geometry Problem 820: Triangle with Cevian

Geometry Problem 820

Triangle, Cevian, Angles, 30 Degrees.

Geometry Problem 819: Quadrilateral and Triangle

Geometry Problem 819

Quadrilateral, Triangle, Angles, 30 degrees.

Geometry Problem 814: Two Equilateral Triangles

Geometry Problem 814

Two Equilateral Triangles with a common Vertex, Angle.

Geometry Problem 761: Scalene Triangle with 60 degrees

Geometry Problem 761

Scalene Triangle with an angle of 60 degrees, Euler Line, Equilateral Triangle.

Geometry Problem 754: Equilateral Triangle

Geometry Problem 754

Equilateral Triangle, Center, Angle, 60 Degrees, Perimeter.

Geometry Problem 698: Quadrilateral and Triangle

Geometry Problem 698

Quadrilateral, Diagonal, Angle Bisector, Triangle, 120 Degrees.

Geometry Problem 670: Triangle with 60 degrees

Geometry Problem 670

Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Congruence.