College Geometry Online, eLearning

Online Geometry: Parallel Lines, Theorems and Problems
 

Parallel Lines, Page 4

Parallel Lines Index

 

Circular Segments, Inscribed Squares

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

Circle, Chord, Tangent, Perpendicular

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

Inscribed Quadrilateral

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

Triangle, Parallel, Congruence, Similarity

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. 

Triangle, Parallel, Congruence, Similarity

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

Euclid Elements Book X, Lemma for Proposition 33

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

Quadrilateral, Perpendicular, Squares, Area

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

Problem 273 Triangle and Squares

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

Rectangle, Isosceles Right Triangle, Square, Area

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

Elearning 251: Parallelogram

Proposed Problem 251.
Parallelogram, sides, diagonals, squares, areas.

Elearning 245: Parallelogram

Proposed Problem 245. Parallelogram with Equilateral triangles

Quadrilateral, midpoints

Proposed Problem 237. Quadrilateral, Midpoints, Exterior line, Perpendicular lines, Parallel lines.

Quadrilateral, midpoints

Proposed Problem 236. Quadrilateral, Midpoints, Exterior line, Perpendicular lines, Parallel lines.

Problem about Parallelogram and transversal

Proposed Problem 235. Parallelogram, Transversal line, Perpendicular lines, Parallel lines.  

Problem 233: Parallelogram

Proposed Problem 234. Parallelogram, Line through a vertex, Perpendicular lines, Parallel lines.

Elearn 232: Parallelogram

Proposed Problem 233. Parallelogram, Exterior line, Perpendicular lines, Parallel lines.

Elearn 232: Parallelogram, perpendicular lines

Proposed Problem 232. Parallelogram, Line through a vertex, Perpendicular lines.

Elearn 231: Triangle, Midpoint

Proposed Problem 231. Triangle, Midpoints, Transversal, Perpendicular lines, Parallel lines.

Elearn 230: Triangle, Midpoint, Transversal

Proposed Problem 230. Triangle, Midpoints, Transversal, Perpendicular lines.

Elearn 229: Triangle, Centroid, Transversal

Proposed Problem 229. Triangle, Centroid, Transversal, Perpendicular lines, Parallel lines.

Elearn 228: Triangle, Midpoint

Proposed Problem 228. Triangle, Midpoints, Exterior line, Perpendiculars lines.

Elearn 227: Triangle, Centroid

Proposed Problem 227. Triangle, Centroid, Exterior line, Perpendicular lines, Parallel lines.  

Problem 226: Triangle, Centroid

Proposed Problem 226. Triangle, Centroid, Perpendicular lines, Parallel lines.  

Viviani theorem, isosceles triangle, extension on the base

Proposed Problem 224. Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base, Parallel lines.  

Viviani theorem, Isosceles triangle

Proposed Problem 223. Viviani's theorem, Isosceles triangle, Altitude, Distances, Parallel lines.  

Viviani theorem, Equilateral triangle, exterior point

Proposed Problem 222. Viviani's theorem, Equilateral triangle, Exterior point, Distances.  

Viviani's theorem I

Proposed Problem 221. Viviani's theorem, Equilateral triangle, Interior point, Distances, Parallel lines.  

Rhombus problem

Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean, Parallel lines.

Elearn 218: Right triangle

Proposed Problem 218. Right triangle, Altitude and Projections, Parallel lines.

Elearn 217: Right triangle, Altitude, Projections

Proposed Problem 217. Right triangle, Altitude and Projections, Parallel lines.

Archimedes Arbelos and Square

Archimedes Arbelos and Square 2. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation, Parallel lines.

Archimedes Arbelos and Square

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation, Parallel lines.

Trapezoid and triangle problem

Proposed Problem 185. Trapezoid, Triangles and Angles, Parallel lines.  

Rhombus, Square, Angle

Proposed Problem 179. Rhombus, Square, Diagonal, Angle, Parallel lines.  

Elearning 177: Parallelogram with midpoints, Area

Proposed Problem 177. Parallelogram with Midpoints, Triangles, Areas, Parallel lines.  

Elearning 172: Trapezoid, Quadrilateral, Area

Proposed Problem 172. Trapezoid, Midpoints, Quadrilaterals, Areas, Parallel lines.  

Elearning 172: Trapezoid, Midpoints, Quadrilaterals, Areas

Proposed Problem 171. Trapezoid, Midpoints, Triangles, Areas, Parallel lines.  

Trapezoid, Triangle, Area

Proposed Problem 170. Trapezoid, Midpoint, Triangle, Area, Parallel lines.  

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

Proposed Problem 169. Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas, Parallel lines.  

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

Proposed Problem 168. Parallelogram, Diagonal, Triangles, Pentagon, Areas, Parallel lines.  

Geometry Problem: Parallelogram, Triangles, Area

Proposed Problem 167. Parallelogram, Diagonal, Triangles, Areas, Parallel lines.  

Geometry Problem: Parallelogram, Triangles, Area

Proposed Problem 166. Parallelogram, Diagonal, Triangles, Areas, Parallel lines.  

Elearning 165: Parallelogram area

Proposed Problem 165. Parallelogram, Diagonal, Triangles, Areas, Parallel lines.  

Elearning 164: Parallelogram, Triangles, Area

Proposed Problem 164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas, Parallel lines.  

Elearning 163 Trapezoid, Triangles, Area

Proposed Problem 163. Trapezoid, Diagonals, Triangles, Areas, Parallel lines.  
Trapezoid Index

Elearning 162 Parallelogram and Triangles Areas

Proposed Problem 162. Parallelogram, Triangles, Areas, Parallel lines.  

Elearning 161 Parallelogram and Octagon Areas

Proposed Problem 161. Parallelogram, Midpoints, Octagon, Areas, Parallel lines.  

Quadrilateral Area, Midpoint

Proposed Problem 146. Varignon's Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter, Parallel lines.

Geometry Problem 145. Elearning Triangle

Proposed Problem 145. Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters.  

Geometry problem 144 Triangle

Proposed Problem 144. Four Triangles, Incircle, Tangent and Parallel to Side, Inradii.

Geometry problem 143

Proposed Problem 143. Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii.

Elearning 142: Triangle area

Proposed Problem 142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas.

Elearning 141

Proposed Problem 141. Triangle, Incircle, Tangent , Parallel, Perimeters.

Geometry Problem 137

Proposed Problem 137. Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram.  

Geometry Problem 135

Proposed Problem 135. Orthic Triangle, Altitudes, Perpendicular, Parallel.  

Trapezoid

Trapezoid, Triangle, Diagonals, Midpoints. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
 Parallel lines. Prove proposition.

Elearn 127: Centroid, Incenter

Proposed Problem 127. Centroid and Incenter of a Triangle, Parallel lines, Proportions.

Angle Bisector Theorem

Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem
Parallel lines.

Bottema Theorem. Elearning.

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.

Proposed Problem 112. Area of square and triangle.
 Parallel lines.

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 Last updated: Sep 2, 2022