### 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