Amsco Integrated Algebra I: Angles and Parallel Lines

This is a free lesson from our course in Amsco's Integrated Algebra

This lesson explains about parallel lines and interior, exterior, alternate
interior and exterior, and corresponding angles. Two or more lines are called parallel
lines if and only if the lines lie in the same plane but do not intersect. The symbol
used for parallel lines to each other is ||. E.g. Line AB is parallel to CD is represented
by AB || CD. When two lines are parallel, they have no points in common.
A transversal is a line that intersects two or more lines (in the same plane). When
lines intersect, angles are formed in several locations and names of certain angles
describe ‘where’ the angles are located in relation to the lines. These names describe
angles regardless of the lines being parallel or not parallel. (More text below video...)

(Continued from above)
When two lines are
cut by a third line i.e. traversal, two set of angles, each containing four angles,
are formed. Such angles are: interior angles, exterior angles, alternate interior
angles, alternate exterior angles, interior angles on the same side of the transversal,
corresponding angles.
Note: the word interior means between the lines, the word exterior means outside
the lines and the word alternate means ‘alternating sides’ of the transversal. There
are other angle relationships also occurring when working with parallel lines. E.g.
vertical angles, which are always equal (whether you have parallel lines or not),
and are congruent.
Remember it!
Alternate Interior Angles and Parallel Lines: statement without proof- If two parallel
lines are cut by a transversal, then the alternate interior angles that are formed
have equal measures, i.e. they are congruent.
Corresponding Angles and Parallel Lines: theorem- If two parallel lines are cut
by a transversal, then the corresponding angles formed have equal measures, that
is, they are congruent. Alternate Exterior Angles and Parallel Lines: theorem- If
two parallel lines are cut by a transversal, then the alternate exterior angles
formed have equal measures, that is, they are congruent. Interior Angles on the
Same Side of the Transversal: theorem- If two parallel lines are cut by a transversal,
then the sum of the measures of the interior angles on the same side of the transversal
is 180°.
The video above will explain about angles and parallel lines in detail with the
help of figures and examples.

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