A Transversal
is a line that crosses two parallel lines. In the figure below, A and
B are parallel lines. Note the following when a transversal cuts two
parallel lines:
*the four acute angles will be equal
*the four obtuse angles will also be equal
*each acute angle is supplementary to eacy obtuse angle
If a transversal
intersects two lines such that corresponding angles are congruent, then
the lines are parallel. AND, If two lines are intersected by a transversal
such that interior angles on the same side of the transversal are supplementary,
then the lines are parallel. (See above Transversal)
Using
the above figure - Remember the following:
A transversal
will create eight angles when it intersects two parallel lines.
1. There
will be 2 pairs of alternate angles:
F = H
G = I
2. There
will be 2 pairs of interior angles:
F + I
= 180°
G + H
= 180°
3. There
will be 4 pairs of corresponding angles.
E = I
F = J
D = H
G = K
On your
own, find the angle measure of both x and y and explain
why using the above properties:
Answer:
x = 70°
y =
110°
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