### Definitions

If two parallel lines are transected by a third line,

the angles which are inside the parallel lines and on alternate sides of the third line are called alternate interior angles.

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If two parallel lines are transected by a third line,

the angles which are on the same side of the third line and on corresponding sides of the parallel lines are called corresponding angles.

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If two parallel lines are transected by a third line,

the angles which are inside the parallel lines and on the same side of the third line are called opposite interior angles.

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Two figures are said to be congruent if one can be moved to another by an invertible isometry.

If the three angles in one triangle are congruent to the three angles in another triangle, the two triangles are said to be similar.

In similar triangles sides which are opposite congruent angles are called corresponding sides.

The length of a line segment is the distance between its endpoints.

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Analytic Foundations of Geometry

R. S. Wilson