Notes
angles and parallel lines

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Parallel Lines

Two lines are parallel if one is a translate of the other. That is, one can be obtained from the other by a translation.

Two line segments are parallel if their extensions are parallel. That is, if one can be translated so that it overlays the other.

Angles and Parallel Lines

When a line (called the transversal) crosses two parallel lines then many angles are formed and there are many relationships between these angles.

Corresponding Angles

These are angles that are related by translating one angle along the transversal so that it coincides with the other.

Corresponding angles are always equal.

Alternate Angles

These are angles that are related by translating, as for corresponding angles, and then a half turn, so that the angles in an alternate pair are related to a pair of corresponding angles by taking the angle vertically opposite to one of them.

Alternate angles are always equal.

Cointerior Angles

Cointerior angles are the two angles formed inside the diagram on the same side of the transversal line.

Cointerior angles add up to 180 ∘180^\circ.

Revised on June 23, 2021 21:38:24 by Andrew Stacey
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