In this lesson you’ll be introduced to the definition, basics and uses of parallel
lines and Transversals in geometry. You’ll learn
it in the presentation by instructor in own handwriting, using video and with the
help of several examples with solution. It will be followed by explaining their
use to help you solve problems.
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), each at a different
point.
(More text below video...)
(Continued from above)
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.
Transversal Postulate: This rule involves angles and transversals i.e. if a transversal
intersects two parallel lines, the corresponding angles are congruent. For example:
Given AB
CD and
1 measures 60°.
Find other angles in the figure below:
You can solve this problem, using the following steps,
• since,
1 measures 60°,
2 shall be 120°
(this being supplementary to
1). By definition,
the supplementary angles are any two angles when they sum up to 180°.
•
1 and
3 are Vertical
Angles, as they two nonadjacent angles formed by two intersecting lines. Therefore,
3 = 60°. Then
4 = 120°(this being,
supplementary to
1).
•
1 and
5 are equal (by
transversal postulate)
• similarly,
6=2,
7=3
and
8=4
(by transversal postulate).
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