Download Math 366 Lecture Notes Section 11.3 – More About Angles

Section 11-3
Math 366 Lecture Notes
Section 11.3 – More About Angles
Vertical angles are pairs of angles opposite each other at the intersection of two lines.
Theorem 11-1
Vertical angles are congruent.
Proof:
Supplementary angles are two angles, the sum of whose measures is 180°. Each angle is a
supplement of the other.
Complementary angles are two angles, the sum of whose measures is 90°. Each angle is a
complement of the other.
A line that intersects a pair of lines in a plane is a transversal of those lines.
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same Side Interior Angles
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Section 11-3
Angles and Parallel Lines Theorem
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.
Corollary
If any two distinct coplanar lines are cut by a transversal, then a pair of same side interior angles
are supplementary iff the lines are parallel.
Constructing Parallel Lines
Architects use the fact that lines are parallel iff their corresponding angles are congruent.
We will use corresponding angles in constructing parallel lines in chapter 12.
The Sum of the Measures of the Interior Angles of a Convex Polygon with n Sides
Theorem 11-2
The sum of the measures of the interior angles of a triangle is 180°.
Theorem 11-3
The sum of the measures of the exterior angles (one at each vertex) of a convex polygon is 360°.
Theorem 11-4
a. The sum of the measures of the interior angles of any convex polygon with n sides is
180n – 360, or (n – 2)180°.
180n − 360
b. The degree measure of a single interior angle of a regular n-gon is
, or
n
(n − 2)180
.
n
You go 1 mile south, next 1 mile east, then 1 mile north. You are back to where you started.
You see a bear. What color is it and why?
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