

Online Geometry: Parallel Lines, Theorems and Problems


Parallel Lines, Page 4




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 nonEuclidean 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. 

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

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

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


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


Proposed Problem 245. Parallelogram with Equilateral triangles


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


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


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


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


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


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


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


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


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

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


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

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

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


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

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

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

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


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


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


Archimedes Arbelos and Square 2.
Dynamic Geometry Software.
StepbyStep construction, Manipulation, and animation,
Parallel lines. 

Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
StepbyStep construction, Manipulation, and animation,
Parallel lines. 

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


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


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

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


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


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


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


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


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


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


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


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


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

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


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


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

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

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

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

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

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

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

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

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

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


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

Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
StepbyStep construction, Manipulation, and animation.
Parallel lines. 

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