# Online Geometry: Parallel Lines, Theorems and Problems

## Parallel Lines, Page 3

Geometry Problem 990.
Triangle, Incircle, Median, Cevian, Central Angle, Congruence, Circle, Secant, Midpoint, Parallel.

Geometry Problem 987.
Triangle, Circumcircle, Incenter, Chord, Parallel, Circle, Tangent. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus).

Geometry Problem 980.
Equilateral Triangle, Vertices, Three Parallel, Equal Circles, Construction.

Geometry Problem 973.
Three Parallel, Square, Vertices, Distance Between Two Parallel Lines, Side, Metric Relations.

Geometry Problem 972.
Equilateral Triangle, Vertices, Three Parallel, Equal Circles, Perpendicular Bisector.

Geometry Problem 951.
Intersecting Circles, Chord, Diameter, Parallel, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 947.
Triangle, Circumcircle, Angle Bisector, Chord, Arc, Parallel.

Geometry Problem 946.
Triangle, Quadrilateral, Area, Diagonal, Midpoint, Parallel.

Geometry Problem 944.
Triangle, Orthocenter, Altitude, Perpendicular, 90 Degrees, Parallel Lines.

Geometry Problem 943.
Triangle, Incircle, Inscribed Circle, Tangency Points, Parallel, Metric Relations.

Geometry Problem 940.
Circle, Tangent, Secant, Chord, Parallel, Perpendicular, 90 Degrees, Midpoint.

Geometry Problem 939.
Circle, Tangent, Secant, Chord, Parallel, Midpoint.

Geometry Problem 925.
Cyclic Quadrilateral, Diagonal, Circle, Angle Bisector, Parallel.

Geometry Problem 919.
Rhombus, Triangle, Perpendicular, 90 Degrees, Congruence.

Geometry Problem 914.
Triangle, Orthocenter, Angle Bisector, Parallel Lines, Midpoint.

Geometry Problem 895
Triangle, Incircle, Tangency Points, Parallel line, Collinear Points.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 894
Triangle, Angle, 60 degrees, Incenter, Midpoint, Parallel Lines.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 865
Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity.

Geometry Problem 863
Circumscribed trapezoid, Inscribed Circle, Tangent, Metric Relations.

Geometry Problem 862:
Trapezoid, Parallel, Equal Areas, RMS, Root Mean Square
.

Geometry Problem 861
Triangle, Incircle, Parallel, Tangent, Metric Relations.

Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence.

Geometry Problem 829
Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations.

Geometry Problem 854
Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines.

Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter.

Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle.

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

Geometry Problem 785
Equilateral Triangle, Parallel, Perpendicular.

Geometry Problem 774
Triangle, Two Altitudes, Circumcircle, Tangent at a Vertex, Parallel.

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

Geometry Problem 763
Parallelogram, Diagonal, Parallel, Congruence.

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

Geometry Problem 751.
Parallelogram, Congruence, Intersecting Lines, Angle Bisector.

Geometry Problem 750.
Complete Quadrilateral, Triangle, Diagonal, Parallel, Similarity, Metric Relations.

Geometry Problem 749.
Triangle, Rhombus, Parallel, Harmonic Means, Metric Relations.

Geometry Problem 747.
Trapezoid, Diagonals, Parallel, Bases, Midpoint, Similarity, Harmonic Mean, Metric Relations.

Geometry Problem 746.
Triangle, Cevian, Parallel, Similarity, Harmonic Mean, Metric Relations.

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

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

Proposed Problem 316.
Circular segments and Inscribed Squares.
Parallel lines.

Proposed Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.
Parallel lines.

Proposed Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity, Parallel lines.

Proposed Problem 292.
Triangle, Parallel, Congruence, Similarity.

Archimedes' Book of Lemmas Proposition 1.
Tangent circles and parallel diameters

Archimedes' Book of Lemmas Proposition 10
Tangents to a circle, secant line and chords,
Parallel lines.

Archimedes' Book of Lemmas Proposition 13
Circle, Diameter, Chord, Perpendicular, Congruence
, Parallel lines.

Hyperbolic Tessellation and Geometric Art.
Hyperbolic geometry is a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane.

Proposed Problem 292.
Triangle, Parallel lines, Congruence, Similarity.

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

Engineering the Impossible: Chartres Cathedral
Circle, Square, Triangle, Parallel lines.

Proposed Problem 280.
Quadrilateral, Perpendiculars, , Parallel lines, Area of Squares.

IC 4406: A Seemingly Square Nebula,
Evidence indicates that IC 4406 is likely a hollow cylinder, with its square appearance the result of our vantage point in viewing the cylinder from the side.
Credit: C. R. O'Dell (Vanderbilt U.) et al., Hubble Heritage Team, NASA.
Parallel lines.

Piet Mondrian, New York City 1941-42 and the Golden Rectangle.
Index.
Parallel lines.

Piet Mondrian, Lozenge Composition with Red, Black, Blue, and Yellow 1925,
Pioneer of Geometric abstraction.

Proposed Problem 273.
Triangle, Perpendiculars, Parallel lines, Area of Squares.

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

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