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Chapter 9: Introductory Geometry
9.3 More About Angles
9.3.1. Vocabulary
9.3.1.1. vertical angles – appear any time two lines intersect; any two nonadjacent angles are congruent
9.3.1.2. supplementary angles – sum of the angles is 180o
9.3.1.3. complementary angles – sum of the angles is 90o
9.3.1.4. transversal – a line that intersects a pair of lines
9.3.1.5. interior angles – between the two lines intersected by the
transversal
9.3.1.6. exterior angles – outside the two lines intersected by the
transversal
9.3.1.7. alternate interior angles – congruent when transversal cuts through
two parallel lines
9.3.1.8. alternate exterior angles – congruent when transversal cuts through
two parallel lines
9.3.1.9. corresponding angles – congruent angles on top of the parallel
lines on the same side of the transversal – see fig. 9-21 p. 524 and
table 9-8
9.3.2. Theorem 9-2: Vertical angles are congruent
9.3.3. Sums of angles
9.3.3.1. See Table 9-7 p. 523
9.3.3.2. Supplementary angles sum to 180o
9.3.3.3. Complimentary angles sum to 90o
9.3.4. Two lines cut by a transversal
9.3.4.1. See figure 9-21
9.3.4.2. interior angles
9.3.4.3. exterior angles
9.3.4.4. alternate interior angles
9.3.4.5. alternate exterior angles
9.3.4.6. corresponding angles
9.3.5. Theorem 9-3: If any two distinct coplanar lines are cut by a transversal,
then a pair of corresponding angles, alternate interior angles, or alternate exterior
angles are congruent if, and only if, the lines are parallel
9.3.6. The sum of the measures of the angles of a triangle
9.3.6.1. sum of the measures of the interior angles of a triangle is 180o
9.3.6.2. sum of the measures of the exterior angles of a triangle is 360 o
9.3.6.3. sum of the measures of the exterior angles of any convex polygon
is 360o
9.3.7. Theorem 9-4: The sum of the measures of the interior angles of a triangle
is 180o
9.3.8. Now try this 9-10: p. 526
9.3.9. Theorem 9-5: The sum of the measures of the exterior angles of a convex
polygon is 360o
9.3.10. Now try this 9-11: p. 528
9.3.11. The sum of the measures of the interior angles of a convex polygon
with n sides
9.3.11.1. Theorem 9-6:
 The sum of the measures of the interior angles of a convex
polygon with n sides is 180n – 360 or (n – 2)180o
 The measure of a single interior angle of a REGULAR n-gon is
n  2180
180n  360
or
n
n
9.3.12. Now try this 9-12: p. 529
9.3.13. Ongoing Assessment p. 529
9.3.13.1. Home work: 1,2ac, 3ac, 5a, 6ac, 8ac, 9ac, 10a, 14, 16, 18a