![](../landscape/landscape_px1.gif) |
|
![College Geometry Online, eLearning](../machu_picchu_h1_910.jpg)
Online Geometry: Parallel Lines, Theorems and Problems
|
|
Parallel Lines, Page 4
|
![Parallel Lines Index](parallel_lines_index_17.jpg) |
|
![Circular Segments, Inscribed Squares](../problem/p316_circle_squares_17.jpg) |
Proposed Problem 316.
Circular segments and Inscribed Squares.
Parallel lines. |
![Circle, Chord, Tangent, Perpendicular](../problem/p313_tangent_chord_17.jpg) |
Proposed Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.
Parallel lines. |
![Inscribed Quadrilateral](../problem/p293_inscribed_quadrilatera.jpg) |
Proposed Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right
triangle, Area, Similarity, Parallel lines. |
![Triangle, Parallel, Congruence, Similarity](../problem/p292_triangle_parallel_17.jpg) |
Proposed Problem 292.
Triangle, Parallel, Congruence, Similarity. |
![](../ArchBooLem01_170.jpg) |
Archimedes' Book of Lemmas
Proposition 1.
Tangent circles and parallel diameters |
![](../ArchBooLem10_170.jpg) |
Archimedes' Book of Lemmas
Proposition 10
Tangents to a circle, secant line and chords,
Parallel lines. |
![](../ArchBooLem13_170.jpg) |
Archimedes' Book of Lemmas
Proposition 13
Circle, Diameter, Chord, Perpendicular, Congruence,
Parallel lines. |
![](../geometric_art/hyperbolic_170.jpg) |
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. |
![Triangle, Parallel, Congruence, Similarity](../problem/p292_triangle_parallel_17.jpg) |
Proposed Problem 292.
Triangle, Parallel lines, Congruence, Similarity. |
![Euclid Elements Book X, Lemma for Proposition 33](euclid_book_x_33_17.jpg) |
Euclid's
Elements, Book X, Lemma for Proposition 33
One page visual illustration.
Parallel lines. |
![Quadrilateral, Perpendicular, Squares, Area](../problem/p280_quadrilateral_squares_.jpg) |
Proposed Problem 280.
Quadrilateral, Perpendiculars, , Parallel lines, Area of Squares. |
![Problem 273 Triangle and Squares](../problem/p273_triangle_square_17.jpg) |
Proposed Problem 273.
Triangle, Perpendiculars, Parallel lines, Area of Squares. |
![Rectangle, Isosceles Right Triangle, Square, Area](../problem/p252_rectangle_area_17.jpg) |
Proposed Problem 252.
Rectangle, isosceles right triangle, square, area.
|
![Elearning 251: Parallelogram](../problem/p251_parallelogram_area_17.jpg) |
Proposed Problem 251.
Parallelogram, sides, diagonals, squares, areas.
|
![Elearning 245: Parallelogram](../problem/p245_parallelogram_equilate.jpg) |
Proposed Problem 245. Parallelogram with Equilateral triangles
|
![Quadrilateral, midpoints](http://gogeometry.com/
problem/p237_quadrilateral_17.jpg) |
Proposed Problem 237. Quadrilateral, Midpoints, Exterior line,
Perpendicular lines, Parallel lines.
|
![Quadrilateral, midpoints](http://gogeometry.com/
problem/p236_quadrilateral_17.jpg) |
Proposed Problem 236. Quadrilateral, Midpoints, Exterior line,
Perpendicular lines, Parallel lines.
|
![Problem about Parallelogram and transversal](http://gogeometry.com/
problem/p235_parallelogram_17.jpg) |
Proposed Problem 235. Parallelogram, Transversal line, Perpendicular
lines, Parallel lines.
|
![Problem 233: Parallelogram](../problem/p234_parallelogram_17.jpg) |
Proposed Problem 234. Parallelogram, Line through a vertex,
Perpendicular lines, Parallel lines.
|
![Elearn 232: Parallelogram](http://gogeometry.com/
problem/p233_parallelogram_17.jpg) |
Proposed Problem 233. Parallelogram, Exterior line, Perpendicular
lines, Parallel lines.
|
![Elearn 232: Parallelogram, perpendicular lines](http://gogeometry.com/
problem/p232_parallelogram_problem_.jpg) |
Proposed Problem 232. Parallelogram, Line through a vertex,
Perpendicular lines.
|
![Elearn 231: Triangle, Midpoint](http://gogeometry.com/
problem/p231_triangle_midpoint_17.jpg) |
Proposed Problem 231. Triangle, Midpoints, Transversal,
Perpendicular lines, Parallel lines.
|
![Elearn 230: Triangle, Midpoint, Transversal](http://gogeometry.com/
problem/p230_triangle_midpoint_17.jpg) |
Proposed Problem 230. Triangle, Midpoints, Transversal,
Perpendicular lines.
|
![Elearn 229: Triangle, Centroid, Transversal](http://gogeometry.com/
problem/p229_triangle_centroid_17.jpg) |
Proposed Problem 229. Triangle, Centroid, Transversal, Perpendicular
lines, Parallel lines. |
![Elearn 228: Triangle, Midpoint](http://gogeometry.com/
problem/p228_triangle_midpoint_17.jpg) |
Proposed Problem 228. Triangle, Midpoints, Exterior line,
Perpendiculars lines.
|
![Elearn 227: Triangle, Centroid](http://gogeometry.com/
problem/p227_triangle_centroid_17.jpg) |
Proposed Problem 227. Triangle, Centroid, Exterior line,
Perpendicular lines, Parallel lines. |
![Problem 226: Triangle, Centroid](http://gogeometry.com/
problem/p226_triangle_centroid_17.jpg) |
Proposed Problem 226. Triangle, Centroid, Perpendicular lines,
Parallel lines. |
![Viviani theorem, isosceles triangle, extension on the base](http://gogeometry.com/
problem/p224_viviani_theorem_17.jpg) |
Proposed Problem 224. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Point on the extension of the base, Parallel lines.
|
![Viviani theorem, Isosceles triangle](http://gogeometry.com/
problem/p223_viviani_theorem_17.jpg) |
Proposed Problem 223. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Parallel lines. |
![Viviani theorem, Equilateral triangle, exterior point](http://gogeometry.com/
problem/p222_viviani_theorem_17.jpg) |
Proposed Problem 222. Viviani's theorem, Equilateral triangle,
Exterior point, Distances. |
![Viviani's theorem I](http://gogeometry.com/
problem/p221_viviani_theorem_17.jpg) |
Proposed Problem 221. Viviani's theorem, Equilateral triangle,
Interior point, Distances, Parallel lines. |
![Rhombus problem](http://gogeometry.com/
problem/p219_rhombus_mean_17.jpg) |
Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean,
Parallel lines.
|
![Elearn 218: Right triangle](http://gogeometry.com/
problem/p218_right_triangle_17.jpg) |
Proposed Problem 218. Right triangle, Altitude and Projections,
Parallel lines.
|
![Elearn 217: Right triangle, Altitude, Projections](http://gogeometry.com/
problem/p217_right_triangle_17.jpg) |
Proposed Problem 217. Right triangle, Altitude and Projections,
Parallel lines.
|
![Archimedes Arbelos and Square](http://gogeometry.com/
geometry/arbelos_circle_square_2_17.jpg) |
Archimedes Arbelos and Square 2.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation,
Parallel lines. |
![Archimedes Arbelos and Square](http://gogeometry.com/
geometry/arbelos_circle_square_17.jpg) |
Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation,
Parallel lines. |
![Trapezoid and triangle problem](../problem/p185_trapezoid_angle_17.jpg) |
Proposed Problem 185. Trapezoid,
Triangles and Angles, Parallel lines.
|
![Rhombus, Square, Angle](../problem/p179_rhombus_square_17.jpg) |
Proposed Problem 179. Rhombus,
Square, Diagonal, Angle, Parallel
lines.
|
![Elearning 177: Parallelogram with midpoints, Area](../problem/p177_parallelogram_area_17.jpg) |
Proposed Problem 177.
Parallelogram with Midpoints, Triangles, Areas,
Parallel lines. |
![Elearning 172: Trapezoid, Quadrilateral, Area](../problem/p172_trapezoid_quadrilatera.jpg) |
Proposed Problem 172. Trapezoid,
Midpoints, Quadrilaterals, Areas,
Parallel lines.
|
![Elearning 172: Trapezoid, Midpoints, Quadrilaterals, Areas](../problem/p171_trapezoid_triangle_17.jpg) |
Proposed Problem 171. Trapezoid,
Midpoints, Triangles, Areas, Parallel
lines.
|
![Trapezoid, Triangle, Area](../problem/p170_trapezoid_triangle_17.jpg) |
Proposed Problem 170. Trapezoid,
Midpoint, Triangle, Area, Parallel
lines.
|
![Geometry Problem: Parallelogram, Triangles, Pentagon, Area](../problem/p169_parallelogram_area_17.jpg) |
Proposed Problem 169.
Parallelogram, Interior and Exterior Points, Diagonals, Pentagon,
Triangles, Areas, Parallel lines.
|
![Geometry Problem: Parallelogram, Triangles, Pentagon, Area](../problem/p168_parallelogram_area_17.jpg) |
Proposed Problem 168.
Parallelogram, Diagonal, Triangles, Pentagon, Areas,
Parallel lines.
|
![Geometry Problem: Parallelogram, Triangles, Area](../problem/p167_parallelogram_area_17.jpg) |
Proposed Problem 167.
Parallelogram, Diagonal, Triangles, Areas,
Parallel lines.
|
![Geometry Problem: Parallelogram, Triangles, Area](../problem/p166_parallelogram_area_17.jpg) |
Proposed Problem 166.
Parallelogram, Diagonal, Triangles, Areas,
Parallel lines.
|
![Elearning 165: Parallelogram area](../problem/p165_parallelogram_area_17.jpg) |
Proposed Problem 165.
Parallelogram, Diagonal, Triangles, Areas,
Parallel lines.
|
![Elearning 164: Parallelogram, Triangles, Area](../problem/p164_parallelogram_area_17.jpg) |
Proposed Problem 164.
Parallelogram, Trapezoid, Diagonal, Triangles, Areas,
Parallel lines.
|
![Elearning 163 Trapezoid, Triangles, Area](../problem/p163_trapezoid_triangle_17.jpg) |
Proposed Problem 163. Trapezoid,
Diagonals, Triangles, Areas, Parallel
lines.
Trapezoid Index |
![Elearning 162 Parallelogram and Triangles Areas](../problem/p162_parallelogram_area_17.jpg) |
Proposed Problem 162.
Parallelogram, Triangles, Areas,
Parallel lines.
|
![Elearning 161 Parallelogram and Octagon Areas](../problem/p161_parallelogram_area_17.jpg) |
Proposed Problem 161.
Parallelogram, Midpoints, Octagon, Areas,
Parallel lines.
|
![Quadrilateral Area, Midpoint](../problem/p146_quadrilateral_area_17.jpg) |
Proposed Problem 146. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter,
Parallel lines. |
![Geometry Problem 145. Elearning Triangle](../problem/p145_four_triangles_circle_.jpg) |
Proposed Problem 145. Four
Triangles, Incircle, Tangent and Parallel to Side, Incenters,
Circumcenters. |
![Geometry problem 144 Triangle](../problem/p144_four_triangles_circle_.jpg) |
Proposed Problem 144. Four
Triangles, Incircle, Tangent and Parallel to Side, Inradii. |
![Geometry problem 143](../problem/p143_four_triangles_circle_.jpg) |
Proposed Problem 143. Four
Triangles, Incircle, Tangent and Parallel to Side, Circumradii. |
![Elearning 142: Triangle area](../problem/p142_four_triangles_area_17.jpg) |
Proposed Problem 142. Four
Triangles, Incircle, Tangent and Parallel to Side, Areas. |
![Elearning 141](../problem/p141_four_triangles_incircl.jpg) |
Proposed Problem 141. Triangle,
Incircle, Tangent , Parallel, Perimeters. |
![Geometry Problem 137](../problem/p137_orthic_triangle_17.jpg) |
Proposed Problem 137.
Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points,
Parallelogram. |
![Geometry Problem 135](../problem/p135_orthic_triangle_17.jpg) |
Proposed Problem 135. Orthic
Triangle, Altitudes, Perpendicular, Parallel. |
![Trapezoid](trapezoid_diagonal_01_17.jpg) |
Trapezoid,
Triangle, Diagonals, Midpoints.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Parallel lines. Prove proposition. |
![Elearn 127: Centroid, Incenter](../problem/p127_centroid_incenter_17.jpg) |
Proposed Problem 127. Centroid
and Incenter of a Triangle, Parallel
lines, Proportions.
|
![Angle Bisector Theorem](euclid_elements_vi_3_bisect.jpg) |
Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem
Parallel lines. |
![Bottema Theorem. Elearning.](bottema_theorem_elearning.jpg) |
Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Parallel lines. |
![Area of Square and triangle, Elearning.](../problem/p112_area_triangle_elearn_17.jpg) |
Proposed Problem 112. Area of
square and triangle.
Parallel lines. |
Go to Page:
Previous |
1 |
2 |
3 |
4 |
5 |
Next
|
|
|
|
|
|
![](../landscape/landscape_bg_right.gif) |
![](../landscape/landscape_px1.gif) |