###### Answer: plane and line

2) In definition 15 he introduces parallel lines in this way; “Straight lines which have the same direction but are not parts of the same straight line are called parallel lines .” Wilson (1868 p. 12) Augustus De Morgan reviewed this text and declared it a failure primarily on the basis of this definition and the way Wilson used it to prove …

In the context of determining parallelism in Euclidean geometry a transversal is a line that intersects two other lines that may or not be parallel to each other. For more general algebraic curves lines could also be: i-secant lines meeting the curve in i points counted without multiplicity or

Parallel – Wikipedia

Parallel (geometry) – Wikipedia

Non-Euclidean geometry – Wikipedia

Parallel (geometry) – Wikipedia

Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. The diagonals bisect each other. One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent triangles.

In Euclidean geometry the lines remain at a constant distance from each other (meaning that a line drawn perpendicular to one line at any point will intersect the other line and the length of the line segment joining the points of intersection remains constant) and are known as parallels.

Undefined terms . In ancient times geometers attempted to define every term . For example Euclid defined a point as “that which has no part”. In modern times mathematicians recognize that attempting to define every word inevitably leads to circular definitions and therefore leave s…