In the figure below, four interior anglesare formed.
Interior angles- , , , and
In the figure below, two pairs of alternate interior anglesare formed.
Alternate interior angles- and
- 3 and 6
4 5
3 4 5 6
9.2 Parallel and Perpendicular Lines 727l 3l 1l (^212)
3 4
(^56)
(^78)
Transversal
l 3
l 1
l (^212)
3 4
(^56)
(^78)
Transversal
Alternate Interior Angles
If two lines are cut by a transversal, then the nonadjacent angles on opposite
sides of the transversal and on the interior of the two lines are called alternate
interior angles.
Success Tip Alternate interior angles are easily spotted because they form a
Z-shape or a backward Z-shape, as shown below.
EXAMPLE (^1) Refer to the figure. Identify:
a.all pairs of corresponding angles
b.all interior angles
c.all pairs of alternate interior angles
StrategyWhen two lines are cut by a transversal,
eight angles are formed. We will consider the relative
position of the angles with respect to the two lines and
the transversal.
WHYThere are four pairs of corresponding angles, four interior angles, and two
pairs of alternate interior angles.
Self Check 1
Refer to the figure below. Identify:
a.all pairs of corresponding
angles
b.all interior angles
c.all pairs of alternate interior
angles
21
(^34)
(^65)
(^78)
Transversal
(^17)
8
2
(^35)
6
4
Now TryProblem 21