Geometry Theorems and Problems - Recent Additions (Page 9 of 15)

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

Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS)

Euclid's Elements Book I, Proposition 3: Given two unequal straight lines, to cut off from the greater a straight line equal to the less

Euclid's Elements Book I, Proposition 2: To place at a given point (as an extremity) a straight line equal to a given straight line

Euclid's Elements Book I, Proposition 1: On a given finite line to construct an equilateral triangle

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 419.
Triangle, Cevian, Incircle, Excircle, Inradius, Exradius

Proposed Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius.

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

Routh's Theorem - Index
Triangle, Cevians, Area, Ratio.
 

Routh's Theorem 1.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 2.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 3.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 4.
Triangle, Cevians, Ratio of Areas.

Proposed Problem 416.
Triangle, Cevians, Trisectors, Area.

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

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

Proposed Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, 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 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

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

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

Concurrent lines.
Theorems and Problems Index.

Proposed Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines.

Median of a Trapezoid, Theorems and Problems. Index.

Circular Sector. Index.
Theorems and Problems. 

Proposed Problem 403.
Circular sector, 90 degrees, Circle, Semicircle, Area.

Proposed Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity.

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.

Points, Theorems and Problems - Index.

Proposed Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Proposed Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.

Proposed Problem 398.
Parallelogram, Area, Similarity, Congruence.

Proposed Problem 397.
Triangle, Altitude, Midpoints, Congruence.

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

Kosnita's Theorem.
Circumcenters, Concurrent lines.

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Median Index.
Theorems and Problems.

Proposed Problem 392.
Triangle, Parallel lines, Concurrent lines.

Proposed Problem 391.
Triangle, Parallel lines, Collinear points.

Proposed Problem 390.
Triangle, Parallel lines, Collinear points.

Proposed Problem 389.
Triangle, Parallel lines, Harmonic Mean.

Proposed Problem 388.
Triangle, Angle bisector, Perpendicular, Parallel.

Proposed Problem 387.
Triangle, Angle bisector, Perpendicular, Concyclic points.

Proposed Problem 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter, Congruence.

Proposed Problem 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Proposed Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

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.

Chord. Index.
A chord of a circle is the line segment joining two points on the circle. 

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

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

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

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 371.
Square, Inscribed circle, Triangle, Area.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Proposed Problem 369.
Intersecting circles, Chord, Center, Angle, Congruence.

Proposed Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.

Proposed Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.

Proposed Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence.

Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area.

Special Right Triangle 30-60.

Special Right Triangles.

Obtuse Triangle.

Proposed Problem 363.
Right triangle, Congruence, Angles.

Proposed Problem 362.
Circle, Chord, Perpendicular, Equal chords.

Euclid's Elements Book I Word Cloud.

Mascheroni construction with compass alone. Index

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

Proposed Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters.

Proposed Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

Mascheroni construction: Find the center of a circle with compass alone.

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

Euclid's Elements, Book X, Lemma for Proposition 33 One page visual illustration.

Proposed Problem 357.
Square, Exterior point, Triangles, Area.

Proposed Problem 356.
Square, Point inside, Triangles, Area.

Proposed Problem 355.
Circles, Common external tangent, Concyclic points.

Proposed Problem 354.
Rhombus, Square, 45 degrees.

Proposed Problem 353.
Tangential quadrilateral, Diagonals, Incircles, Inradii.

Proposed Problem 352.
Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Proposed Problem 351.
Rhombus, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

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

Proposed Problem 349.
Triangle, Cevian, Incircles, Tangents, Tangency Point.

Proposed Problem 348.
Circles, Common External Tangents, Common Internal Tangent.

Proposed Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points.

Proposed Problem 346.
Equal circles, Tangents, Hexagon, Semiperimeter.

Proposed Problem 345.
Equal circles, Tangents, Concurrent lines, Hexagon, Semiperimeter.

Proposed Problem 344.
Quadrilateral, Extension of sides, Circle, Tangent, Semiperimeter.

Proposed Problem 343.
Hexagon, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 342.
Pentagon, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 341.
Triangle, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point.

Proposed Problem 339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point.

Proposed Problem 338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points.

Proposed Problem 337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points.

Tangent Circles Index
 

Proposed Problem 336.
Two equal circles, a Common Tangent and a Square.

Proposed Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Proposed Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

Midpoints.
Theorems and Problems

Proposed Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent.

Proposed Problem 332.
Cyclic quadrilateral, Ratio of diagonals, Similarity.

Proposed Problem 331.
Square, Point on the Inscribed Circle, Tangency Points.

Proposed Problem 330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter.

Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points.

Proposed Problem 328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint.

Tangential or Circumscribed Quadrilateral: Diagonals, Altitudes Theorem.

Proposed Problem 327.
Right triangle Area, Incircle, Circumcircle, Square.

Proposed Problem 326.
Equilateral triangle, Semicircle, Equal arcs.

Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.

Tangential or Circumscribed Quadrilateral
 

Six Tangential or Circumscribed Quadrilaterals Theorem.

Tangential or Circumscribed Quadrilateral: Pitot Theorem.

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

Proposed Problem 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Altitude Index.
Theorems and Problems.

Proposed Problem 323.
Triangle, Incenter, Circumcenter, Equal circles, Collinearity.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Collinear Points.

Incenter. Index.

Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points.

Proposed Problem 319.
Triangle, Altitudes, Perpendiculars, Collinear points.

Proposed Problem 318.
A Scalene triangle, Altitudes, Collinear points.

Proposed Problem 317.
Right triangle and Inscribed Squares.

Proposed Problem 316.
Circular segments and Inscribed Squares.

Proposed Problem 315.
Three Tangent circles, Common external tangent line, Geometric Mean.

Polygons.

Proposed Problem 287: Regular Octagon.

Octagons.

Proposed Problem 286: Square, Midpoints, Octagon.

Proposed Problem 285: Circular Sector 90 degrees, Semicircles, Circle, Tangent, Radius.

Proposed Problem 284: Circular Sector 90 degrees, Semicircles, Tangent, Radius.

Proposed Problem 283: Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius.

Proposed Problem 282.
Right Triangle, Cevian, Angles, Perpendicular, Congruence.