Chapter 3 CNC Math 59
• Alternate interior angles are equal. If two parallel lines are
intersected by a third line (transversal), then alternate interior angles
are equal to each other. Thus, in Figure 3-11, Angle 3 equals Angle 6,
and Angle 4 equals Angle 5.
• Alternate exterior angles are equal. When two parallel lines are
intersected by a third line (transversal), then alternate exterior angles
are equal to each other. Thus, in Figure 3-11, Angle 1 equals Angle 8,
and Angle 2 equals Angle 7.
• Corresponding angles are equal. When two parallel lines are
intersected by a third line (transversal), then all corresponding angles
are equal. Thus, in Figure 3-11, Angle 1 equals Angle 5, Angle 3
equals Angle 7, Angle 2 equals Angle 6, and Angle 4 equals Angle 8.
• The sum of the interior angles of a triangle is 180°. Thus, in Figure 3-12,
Angle 1 plus Angle 2 plus Angle 3 equals 180°.
• The exterior angle of a triangle is equal to the sum of the two
nonadjacent interior angles. Thus, in Figure 3-13, Angle 4 equals
Angle 1 plus Angle 2.
1 2
T
R
S
Figure 3-9. Two angles with corresponding parallel sides are
equal.
Figure 3-10. A transversal line
perpendicular to one parallel line is
perpendicular to the other parallel
line. Lines R and S are parallel.
1
R
S
2
3 4
5 6
7 8
Figure 3-11. Two parallel lines intersected by a third line form
alternate angles that are equal to each other. Interior Angles 4
and 5 are equal along with 3 and 6. Exterior Angles 1 and 8 are
equal along with 2 and 7.
1 3
2
Figure 3-12. Angles 1, 2, and 3
form a triangle totaling 180°.