Machu Picchu, Geometry Theorems and Problems, Online Education

Geometry Theorems and Problems - Recent Additions (Page 5 of 15)

Euclidean Geometry

Archimedes Book of Lemmas Proposition 6

Geometry Problem 645.
Archimedes Book of Lemmas: Proposition 6
Semicircle, Circle, Perpendicular, Arbelos, Inscribed Circle.

Archimedes Book of Lemmas Proposition 5

Geometry Problem 644.
Archimedes Book of Lemmas: Proposition 5
Semicircle, Circle, Perpendicular, Arbelos, Archimedean Twins.

Archimedes Book of Lemmas Proposition 4

Geometry Problem 643.
Archimedes Book of Lemmas: Proposition 4
Semicircle, Circle, Perpendicular, Arbelos, Area.

Archimedes Book of Lemmas Proposition 4

Arbelos Definition by Archimedes
Three Semicircles, Tangent, Diameters.

Archimedes Book of Lemmas Proposition 3

Geometry Problem 642.
Archimedes Book of Lemmas: Proposition 3
Semicircle, Perpendicular, Arc, Midpoint, Congruence.

Archimedes Book of Lemmas Proposition 2

Geometry Problem 641.
Archimedes Book of Lemmas: Proposition 2
Semicircle, Tangent, Perpendicular, Midpoint.

Archimedes Book of Lemmas Proposition 1

Geometry Problem 640.
Archimedes Book of Lemmas: Proposition 1
Tangent circles and parallel diameters 

Semicircle, Perpendicular, Inscribed Circle, Tangent, Congruence

Geometry Problem 639
Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence.

Perpendicular Bisector Index

Perpendicular Bisector.

Arbelos, Circle, Concyclic Points

Geometry Problem 638
Arbelos and Inscribed Circle: Concyclic Points.

Semicircle, Perpendicular, Inscribed Circle, Tangent, Chord

Geometry Problem 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos.

Semicircle, Perpendicular, Inscribed Circle, Tangent

Geometry Problem 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent.

Semicircle, Perpendicular, Inscribed Circle, Radius

Geometry Problem 635
Semicircle, Diameter, Perpendicular, Inscribed Circle, Radius.

Right triangle, Altitude, Incenter, Area

Geometry Problem 634
Right Triangle, Altitude, Incenters, Areas.

Triangle, Parallel Lines, Intersecting Lines

Geometry Problem 633
Triangle, Parallel Lines, Intersecting Lines.

Triangle, Angle Bisectors, Midpoint, Collinear

Geometry Problem 632.
Triangle, Interior and Exterior Angle Bisectors, Midpoints, Collinear Points.

Triangle, Angle Bisectors, Collinear

Geometry Problem 631.
Triangle, Exterior Angle Bisectors, Collinear Points.

Clawson Point

Clawson Point.
Orthic and Extangents Triangles, Concurrent lines.

Clawson Point Puzzle, Geometry for Kids

Clawson Point Puzzle, Geometry for Kids.
22 Piece Polygons

Incenter by Folding

Triangle Incenter by Folding, Video .
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Circumcenter by Folding

Triangle Circumcenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.
Perpendicular Bisectors.

Triangle, Perpendicular, Intersecting Lines

Geometry Problem 629
Triangle, Perpendicular to Sides, Intersecting Lines, Altitude.

Cyclic quadrilateral, Congruence, Parallel

Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines.

Ten Geometry Problems, Visual Index

Sangaku Japanese Geometry
Seventeenth and nineteenth centuries
.

Orthocenter by Folding

Triangle Orthocenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Centroid by Folding

Triangle Centroid by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Cyclic quadrilateral, Congruence, and Concyclic Points

Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points.

Triangle, Incenter, Excenter, Distance

Geometry Problem 626
Triangle, Distance from the Incenter to an Excenter.

Triangle, Parallel, Angle Bisector

Geometry Problem 625
Triangle, Parallel Lines, Congruence, Angle Bisector.

Triangle, Incenter, Excenter, Similarity

Geometry Problem 624
Triangle, Incenter, Excenter, Incircle, Excircle, Similarity.

Triangle, Incenter, Excenter, Concyclic Points

Geometry Problem 623
Triangle, Incenter, Excenter, Incircle, Excircle, Concyclic Points.

Intersecting Circles

Geometry Problem 622
Square with Perpendiculars, Transversal, Congruence.

Two Parallelograms, Center, Parallel

Geometry Problem 621
Three Rectangles, Diagonals, Centers, Angles.

Three Rectangles, Centers, Angles

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

Triangle Area, 30 Degrees, Incircle

Geometry Problem 619
Triangle Area, 30 Degrees, Incircle, Incenter, Tangent.

Triangle area, 60 degrees

Geometry Problem 618
Triangle Area, 60 Degrees, Incircle, Incenter, Tangent.

Right triangle area

Geometry Problem 617
Right Triangle Area, Incircle, Incenter, Tangent, 90 Degrees.

Parallelogram, Diagonal, Parallel

Geometry Problem 616
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Triangle, Square, Area

Geometry Problem 615
Right Triangle with a Square, Diagonals, Center, Area of Quadrilateral.

Parallelogram, Diagonal, Parallel

Geometry Problem 614
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Triangle, Altitude, Collinearity

Geometry Problem 613
Altitude of a Triangle, Perpendicular, Collinear Points.

Triangle, Altitude, Congruence

Geometry Problem 612
Altitude of a Triangle, Perpendicular, Congruence.

Triangle, Altitude, Collinearity

Geometry Problem 611
Altitude of a Triangle, Perpendicular, Collinear Points, Parallel.

Intersecting Circles, 90 degrees

Geometry Problem 610
Intersecting Circles, Radius, Parallel,
Common Tangent, Angle, 90 Degrees.

Triangle, Perpendiculars, Collinearity

Geometry Problem 609
Triangle, Perpendiculars, 90 Degrees, Collinearity.

Square with Right triangles

Geometry Problem 608
Square with Right Triangles, Metric Relations, Congruence, Measurement.

Intersecting Circles

Geometry Problem 607
Intersecting Circles, Triangles, Metric Relations, Measurement.

Isosceles triangle

Geometry Problem 606
Isosceles Triangles, Perpendicular and Parallel Lines.

Square, Circle, Metric Relation

Geometry Problem 605
Circle, Square, Chord, Perpendicular, Circular Segment, Metric Relations.

Parallelogram Area

Geometry Problem 604
Parallelograms, Triangle, Trapezoid, Area.

Parallelogram, Diagonals

Geometry Problem 603
Parallelogram, Diagonals, Congruence, Concurrency.

Triangle, Angle, Congruence

Geometry Problem 602
Triangle, Angles, 30 and 45 Degrees, Cevian, Congruence.

Cyclic quadrilateral, Incenter, Excenter

Geometry Problem 601
Cyclic Quadrilateral, Incenter, Excenter, Rectangle.

Brianchon Theorem

Brianchon's Theorem in a Circumscribed Hexagon.

Brianchon Corollary

Brianchon Corollary, Circumscribed Hexagon, Concurrency lines.

Carnot's Theorem, Acute Triangle

Carnot's Theorem in an Acute Triangle.

Carnot's Theorem, Obtuse Triangle

Carnot's Theorem in an Obtuse Triangle.

Circle Area, Tangent

Geometry Problem 600
Circle, Area, Tangent, Semicircle, Tangency Point.

Regular Hexagon, Square, Midpoint, Angle, Degrees

Geometry Problem 599
Regular Hexagon, Square, Midpoint, Angle, Degrees.

Trapezoid, Perpendicular, Metric Relation

Geometry Problem 598
Trapezoid, Perpendicular, Equal Angles, Metric Relation.

Quadrilateral, 90 degrees, congruence

Geometry Problem 597
Quadrilateral, Right Triangle, Isosceles, Angle, Congruence.

Quadrilateral, 90 degrees, congruence

Geometry Problem 596
Quadrilateral, Right Triangle, Isosceles, Midpoint.

Triangle, equal angles, metric relations

Geometry Problem 595
Triangle, Equal Angles, Isogonal Conjugate, Similarity.

Online education degree: Open geometry problems

Open Geometry Problems - Index

Triangle, Incircle, Altitude, Incenter, Angle

Geometry Problem 594.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude, Angle, Half the Difference.

Triangle, Circumcircle

Geometry Problem 593.
Triangle, Circumcircle, Collinear Points.

Triangle, Incircle, Inradius, Midpoint, Concurrency

Geometry Problem 592.
Triangle, Incenter, Incircle, Tangency Point, Midpoints, Concurrent Lines, Congruence.

Triangle, Incircle, Inradius, Altitude, Midpoint

Geometry Problem 591.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude.

Triangle, Incenter, Midpoint, Area

Geometry Problem 590.
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Areas.

Triangle, Incenter, Midpoint, Perpendicular

Geometry Problem 589.
Triangle, Incenter, Incircle, Tangency Points, Midpoint, Perpendicular, Distance.

Triangle, Incenter, Midpoints

Geometry Problem 588.
Triangle, Incenter, Incircle, Tangency Points, Midpoints, Distance, Sum.

Triangle, Incenter

Geometry Problem 587.
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Distance, Half the Difference.

Cyclic quadrilateral, Circumcenter, Concurrency

Geometry Problem 586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

Cyclic quadrilateral, Circumcenter, Concurrency

Problem 585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency.

Cyclic quadrilateral, Circumcenter, Parallelogram

Problem 584.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms.

Quadrilateral, Circumcenters

Problem 583.
Quadrilateral, Diagonals, Circumcenters, Parallelogram, Octagon, Areas.

Quadrilateral, Diagonals, Incenters

Problem 582.
Quadrilateral, Diagonals, Incenters, Metric Relations.

Triangula Pyramid, Volume

Problem 581.
Volume of two Triangular Pyramids, Equal Trihedral Angle, Product of three Edges.

Geometry problems 581-590

Geometry Problems 581 - 590.
Quadrilateral, Diagonals, Concurrency, Incenter, Metric Relations, Circumcenters, Parallelogram, Octagon, Areas, Tangency Point, Midpoint, Cyclic Quadrilateral, Volume of two Triangular Pyramids, Equal Trihedral Angle, Product of three Edges.

Triangle Area

Problem 580.
Triangles, Equal Angle, Transversal, Product of Sides, Areas.

Quadrilateral, Diagonal, Area

Problem 579.
Quadrilateral, Diagonals, Triangles, Areas.

Area of a Triangle, Theorems and Problems

Area of a Triangle, Theorems and Problems, Index.

Perpendicular Chords

Problem 578.
Circle, Perpendicular Chords, Midpoints, Curvilinear Triangle, Area, 90 Degrees.

Metric Relations in a Right Triangle

Metric Relations in a Right Triangle, Theorems and Problems.

Isosceles triangle, Circle

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

Diameters and Chords on a Circle

Diameters and Chords, Theorems and Problems. Index.

Centroid, Barycenter

Problem 576.
Centroid, Triangle, Quadrilateral, Parallel, Measurement.

Cyclic quadrilateral, angle bisector, measurement

Problem 575.
Cyclic quadrilateral, Angle bisector, Measurement.

Intersection of a Line with a Circle

Intersection of a Line with a Circle
 

Circle, Chord, Secante, Angle bisector

Problem 574.
Circle, Chord, Secant, Angle Bisector, Perpendicular.

Cyclic quadrilateral, Angle bisector

Problem 573.
Cyclic quadrilateral, Angle bisector, Perpendicular.

Online Math: Geometry Problem 572, Right triangle and Circle

Problem 572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles.

Online Math: Geometry Problem 571, Circle

Problem 571.
Circle, Diameter, Chord, Perpendicular, Measurement.

Online education: Geometry Problem 570, Collinearity

Problem 570.
Square, Center, Right Triangles, Congruence, Collinearity.

Quadrilateral, Excircles

Problem 569.
Quadrilateral, Excircles, Tangency Points, Congruence.

Triangle, Excircles, Congruence

Problem 568.
Triangle, Excircles, Tangency Point, Congruence.

Geometry problems 561-570

Geometry Problems 561 - 570.
Right Triangle, Altitude, Angle Bisector, Congruence, Median, Area, Trisector, 60 Degrees, Equilateral, Parallel, Transversal, Circumcircle, Concyclic, Similarity.

Geometry problems 551-560

Geometry Problems 551 - 560.
Right Triangle, Altitude, Angle Bisector, Congruence, Median, Area, Trisector, 60 Degrees, Equilateral, Parallel, Transversal, Circumcircle, Concyclic, Similarity.

Geometry problem 567

Problem 567.
Right triangle, Incircle, Excircle, Collinear tangency points.

Quadrilateral, Parallel

Problem 566.
Quadrilateral, Diagonals, Parallel.

Triangle, Circle, Congruence, Concyclic points

Problem 565.
Triangle, Isogonal lines, Angles, Congruence, Concyclic Points.

Complete quadrilateral, Circles

Problem 564.
Complete Quadrilateral, Incenter, Excenter, Concyclic Points, Incircle, Excircle.

Pentagon, Rectangle

Problem 563.
Regular Pentagon, Center, Rectangle, Diagonals, Angle.

Math Education: Triangle, Incenter

Problem 562.
Triangle, Cevian, Incenter, Perpendicular, Concyclic Points, Cyclic Quadrilateral.

Triangle, Cevian, Incenters, 90 Degrees

Problem 561.
Triangle, Cevian, Incenter, Incircle, Perpendicular, Tangent.

Triangle, Cevian, Incircles

Problem 560.
Triangle, Cevian, Incenter, Incircle, Perpendicular, Tangent.

Triangle, Incenter, 90 Degrees

Problem 559.
Triangle, Cevian, Incenters, Angle, 90 Degrees.

Wittenbauer Parallelogram

Problem 558.
Quadrilateral, Trisection, Sides, Wittenbauer Parallelogram, Area, Auxiliary Lines.

Varignon Parallelogram

Problem 557.
Quadrilateral, Midpoints, Sides, Varignon Parallelogram, Area, Auxiliary Lines.

Quadrilateral, Diagonal, Angle

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

Parallel lines, Angles

Problem 555.
Parallel lines, Angle Sums.

Concave quadrilateral

Problem 554.
Concave Quadrilateral, Angles, Sum.

Quadrilateral, Angle, Sum

Problem 553.
Quadrilateral, Angles, Sum.

Parallel lines

Problem 552.
Parallel lines, Transversal, Angle Sums.

Parallel lines

Problem 551.
Parallel lines, Transversal, Angle Sums.

Parallel lines

Problem 550.
Parallel lines, Transversal, Angle Sums.

Parallel lines

Problem 549.
Parallel lines, Transversal, Angle Sums.

Triangle, Circumcircles, Circumcenters, Concyclic

Problem 548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points, Similarity.

Triangle, Four circumcircles

Problem 547.
Triangle, Transversal, Four Circumcircles, Concurrency.

Circumcircle Index

Circumcircle Index.

Triangle, Angle Trisectors, Equilateral

Problem 546.
Triangle, Angle Trisectors, 60 Degrees, Equilateral triangle.

Acute Triangle with altitudes and squares

Problem 545.
Acute Triangle, Squares, Altitudes, Area, Measure.

Right Triangle, Altitude, Median, Equal angles, Measure

Problem 544.
Right Triangle, Altitude, Median, Equal angles, Measure.

Geometry problems 341-350

Geometry Problems 341 - 350.
Triangle, Quadrilateral, Pentagon, Hexagon, Inscribed circle, Tangent, Semiperimeter, Equal circles, Concurrent lines, Altitude, Concyclic Points, Cevian, Incircle.

Right Triangle, Altitude, Angle Bisector, Median

Problem 543.
Right Triangle, Altitude, Angle Bisector, Median.

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