Download Chapter 10: Introducing Geometry

Chapter 10: Introducing Geometry
10.3
More About Angles
10.3.1. Angles in Intersecting Lines
10.3.1.1. transversal – a line cutting through two or more distinct lines
10.3.1.2. alternate interior angles – congruent angles formed on opposite
sides of a transversal between the two lines intersected
10.3.1.3. alternate exterior angles – congruent angles formed on opposite
sides of a transversal outside the two lines intersected
10.3.1.4. corresponding angles – congruent angles formed on the same side
of a transversal where one angle is between the two lines including one
line and the other angle is outside including the other line of the two
lines intersected
10.3.1.5. same-side interior angles – same-side interior angles are
supplementary angles
10.3.1.6. same-side exterior angles – same-side exterior angles are
supplementary angles
10.3.1.7. vertical angles – congruent angles formed by the intersection of any
two distinct lines such that opposite pairs of angles are congruent
10.3.2. Angles in Polygons
10.3.2.1. sum of the interior angles of a triangle – the sum of the measures of
the interior angles of a triangle is 180°
10.3.2.2. sum of the interior angles of a quadrilateral – the sum of the
measure of the interior angles of a quadrilateral is 360° because the
diagonal of any quadrilateral divides the quadrilateral into two triangles
10.3.2.3. sum of the interior angles of any polygon – the sum of the
measures of the interior angles of an n-gon is (n – 2) 180°
10.3.2.4. sum of the exterior angles of any polygon – the sum of the exterior
angles of any polygon is 360°
10.3.3. Angles in Regular Polygons
10.3.3.1. interior angle measures for a regular polygon – the measure of
(n − 2 )180°
each interior angle of a regular n-gon is
n
10.3.3.2. exterior angle measures for a regular polygon – the measure of an
360°
exterior angle of a regular n-gon is
n
10.3.3.3. central angle measure for a regular polygon – the measure of the
360°
central angle of a regular n-gon is
n
10.3.4. Angles in Circles
10.3.4.1. arc – portion of a circle cut off by a pair of rays
10.3.4.2. relating arc measure to angle measure –
1
10.3.4.2.1. m∠P =
m(arc s)
2
10.3.4.2.1.1.
angle inside the circle
10.3.4.2.1.2.
angle vertex on circle
1
10.3.4.2.2. m∠P =
[m(arc s) – m(arc r)]
2
10.3.4.2.2.1.
angle outside the circle
1
10.3.4.2.3. m∠P =
[m(arc s) + m(arc r)]
2
10.3.4.2.3.1.
angle inside the circle
10.3.4.2.3.2.
angle vertex NOT on the circle
10.3.5. Problems and Exercises p. 560
10.3.5.1. Home work: 2, 5, 7, 10, 11, 13, 17, 20, 22, 23, 24, 28